Mass Tests Exp1 glm

1 Preferred Experiment

1.1 Across prefs

1.2 Movement Duration

Table 1.1: Movement duration linear models.

Duration	Linear Estimate	P-Value	Std Error
Circle	3.398e-02	0.000e+00	1.018e-03
Pilot	4.066e-02	0.000e+00	5.330e-04
Arc	3.665e-02	0.000e+00	9.492e-04
All	3.764e-02	0.000e+00	4.590e-04

Table 1.1: Movement duration average values (s)

Effective Mass (kg)	2a	2b	2c
2.5	0.764±0.038	0.823±0.031	0.632±0.036
3.8	0.83±0.041	0.881±0.033	0.703±0.034
4.7	0.856±0.042	0.905±0.034	0.741±0.043
6.1	0.89±0.043	0.959±0.036	0.781±0.048

This next stat output shows the a LME with movedur ~ target + eff_mass*exp + (1|subj).

## 
##   Simultaneous Tests for General Linear Hypotheses
## 
## Fit: lmer(formula = movedur ~ factor(targetnum) + eff_mass * factor(exp) + 
##     (1 | subj), data = prefpilot)
## 
## Linear Hypotheses:
##                                   Estimate Std. Error z value Pr(>|z|)    
## (Intercept) == 0                 0.7201709  0.0296551  24.285  < 2e-16 ***
## factor(targetnum)2 == 0         -0.0653049  0.0017152 -38.075  < 2e-16 ***
## factor(targetnum)3 == 0         -0.0067108  0.0017313  -3.876 0.000106 ***
## factor(targetnum)4 == 0         -0.0394681  0.0017155 -23.007  < 2e-16 ***
## eff_mass == 0                    0.0339780  0.0008742  38.866  < 2e-16 ***
## factor(exp)pilot == 0           -0.1469007  0.0382529  -3.840 0.000123 ***
## factor(exp)smallt == 0           0.0442074  0.0418978   1.055 0.291369    
## eff_mass:factor(exp)pilot == 0   0.0067011  0.0011208   5.979 2.25e-09 ***
## eff_mass:factor(exp)smallt == 0  0.0026912  0.0012137   2.217 0.026598 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## (Univariate p values reported)

There is an overall effect of mass on movement duration (slope = 3.398e-02, p = 0.000e+00).

Experiment 2b movement duration is not different from 2a (p = 2.914e-01).

Experiment 2c movement duration is significantly lower than 2a (slope = -1.469e-01, p = 1.229e-04).

The interesting thing with these are the interaction effects.

Experiment 2b movement duration increases with mass more than experiment 2a (slope = 2.691e-03, p = 2.660e-02).

Experiment 2c movement duration increases with mass more than experiment 2a (slope = 6.701e-03, p = 2.245e-09).

Figure 1.1: Movement Duration by experiment.

Figure 1.2: Movement duration broken up by experiment.

1.2.1 Movement Duration Norm

Table 1.2: Movement duration linear models.

Duration	Linear Estimate	P-Value	Std Error
Circle	4.514e-02	0.000e+00	1.355e-03
Pilot	6.376e-02	0.000e+00	8.295e-04
Arc	4.431e-02	0.000e+00	1.157e-03
All	5.286e-02	0.000e+00	6.218e-04

Table 1.2: Movement duration average values (s)

Effective Mass (kg)	2a	2b	2c
2.5	1±0.043	1±0.032	1±0.03
3.8	1.092±0.055	1.073±0.034	1.117±0.039
4.7	1.122±0.05	1.101±0.035	1.171±0.045
6.1	1.168±0.055	1.165±0.036	1.228±0.045

This next stat output shows the a LME with movedur_norm ~ target + eff_mass*exp + (1|subj).

## 
##   Simultaneous Tests for General Linear Hypotheses
## 
## Fit: lmer(formula = movedur_norm ~ factor(targetnum) + eff_mass * 
##     factor(exp) + (1 | subj), data = prefpilot)
## 
## Linear Hypotheses:
##                                   Estimate Std. Error z value Pr(>|z|)    
## (Intercept) == 0                 0.9398696  0.0180023  52.208  < 2e-16 ***
## factor(targetnum)2 == 0         -0.0898485  0.0023155 -38.804  < 2e-16 ***
## factor(targetnum)3 == 0         -0.0089995  0.0023373  -3.850 0.000118 ***
## factor(targetnum)4 == 0         -0.0550772  0.0023159 -23.782  < 2e-16 ***
## eff_mass == 0                    0.0451272  0.0011802  38.236  < 2e-16 ***
## factor(exp)pilot == 0           -0.0409605  0.0231456  -1.770 0.076779 .  
## factor(exp)smallt == 0          -0.0061003  0.0253361  -0.241 0.809730    
## eff_mass:factor(exp)pilot == 0   0.0186385  0.0015130  12.319  < 2e-16 ***
## eff_mass:factor(exp)smallt == 0 -0.0008113  0.0016385  -0.495 0.620481    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## (Univariate p values reported)

There is an overall effect of mass on movement duration (slope = 4.513e-02, p = 0.000e+00).

Experiment 2b movement duration is not different from 2a (p = 8.097e-01).

Experiment 2c movement duration is not different from 2a (p = 7.678e-02).

The interesting thing with these are the interaction effects.

Experiment 2b movement duration did NOT change with mass more than 2a. (p = 6.205e-01).

Experiment 2c movement duration increases with mass more than experiment 2a (slope = 1.864e-02, p = 0.000e+00).

(#fig:movedur_normbyexperiment)Movement Duration by experiment.

(#fig:movedur_norm1)Movement duration broken up by experiment.

1.3 Peak Velocity

Table 1.3: Peak Velocity linear models.

Velocity	Linear Estimate	P-Value	Std Error
Circle	-1.364e-02	0.000e+00	3.095e-04
Pilot	-2.052e-02	0.000e+00	3.331e-04
Arc	-1.187e-02	0.000e+00	2.224e-04
All	-1.608e-02	0.000e+00	1.810e-04

Table 1.3: Peak Velocity average values (m/s)

Effective Mass (kg)	2a	2b	2c
2.5	0.264±0.076	0.23±0.066	0.393±0.093
3.8	0.235±0.068	0.208±0.06	0.347±0.082
4.7	0.225±0.065	0.201±0.058	0.334±0.079
6.1	0.213±0.061	0.185±0.054	0.315±0.074

This next stat output shows the a LME with movedur ~ target + eff_mass*exp + (1|subj).

## 
##   Simultaneous Tests for General Linear Hypotheses
## 
## Fit: lmer(formula = peakvel_target ~ factor(targetnum) + eff_mass + 
##     eff_mass * factor(exp) + (1 | subj), data = prefpilot)
## 
## Linear Hypotheses:
##                                   Estimate Std. Error z value Pr(>|z|)    
## (Intercept) == 0                 0.2779341  0.0173622  16.008  < 2e-16 ***
## factor(targetnum)2 == 0          0.0204180  0.0006711  30.425  < 2e-16 ***
## factor(targetnum)3 == 0          0.0100581  0.0006774  14.847  < 2e-16 ***
## factor(targetnum)4 == 0          0.0234736  0.0006712  34.971  < 2e-16 ***
## eff_mass == 0                   -0.0136629  0.0003421 -39.942  < 2e-16 ***
## factor(exp)pilot == 0            0.1426530  0.0224063   6.367 1.93e-10 ***
## factor(exp)smallt == 0          -0.0349980  0.0245432  -1.426 0.153875    
## eff_mass:factor(exp)pilot == 0  -0.0068836  0.0004385 -15.697  < 2e-16 ***
## eff_mass:factor(exp)smallt == 0  0.0017847  0.0004749   3.758 0.000171 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## (Univariate p values reported)

There is an overall effect of mass on peak velocity (slope = -1.366e-02, p = 0.000e+00).

Experiment 2b peak velocity is not different from 2a (p = 1.539e-01).

Experiment 2c peak velocity is significantly greater than 2a (slope = 1.427e-01, p = 1.932e-10).

The interesting thing with these are the interaction effects.

Experiment 2b peak velocity increases with mass more than experiment 2a (slope = 1.785e-03, p = 1.712e-04).

Experiment 2c peak velocity decreases with mass more than experiment 2a (slope = -6.884e-03, p = 0.000e+00).

Figure 1.3: Peak Velocity by experiment.

Figure 1.4: Peak velocity broken by experiment.

1.3.1 Peak Velocity Normalized

## Warning in checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, :
## Model failed to converge with max|grad| = 0.00287782 (tol = 0.002, component 1)

Table 1.4: Peak Velocity linear models.

Velocity	Linear Estimate	P-Value	Std Error
Circle	-5.037e-02	0.000e+00	1.143e-03
Pilot	-5.158e-02	0.000e+00	8.120e-04
Arc	-5.225e-02	0.000e+00	9.490e-04
All	-5.152e-02	0.000e+00	5.524e-04

Table 1.4: Peak Velocity average values (m/s)

Effective Mass (kg)	2a	2b	2c
2.5	1±0.289	1±0.289	0.393±0.093
3.8	0.896±0.259	0.906±0.261	0.347±0.082
4.7	0.855±0.247	0.874±0.252	0.334±0.079
6.1	0.815±0.235	0.806±0.233	0.315±0.074

This next stat output shows the a LME with movedur ~ target + eff_mass*exp + (1|subj).

## 
##   Simultaneous Tests for General Linear Hypotheses
## 
## Fit: lmer(formula = peakvel_target_norm ~ factor(targetnum) + eff_mass + 
##     eff_mass * factor(exp) + (1 | subj), data = prefpilot)
## 
## Linear Hypotheses:
##                                  Estimate Std. Error z value Pr(>|z|)    
## (Intercept) == 0                 1.057777   0.018194  58.138   <2e-16 ***
## factor(targetnum)2 == 0          0.078438   0.002066  37.974   <2e-16 ***
## factor(targetnum)3 == 0          0.036508   0.002085  17.509   <2e-16 ***
## factor(targetnum)4 == 0          0.084430   0.002066  40.867   <2e-16 ***
## eff_mass == 0                   -0.050428   0.001053 -47.897   <2e-16 ***
## factor(exp)pilot == 0            0.005151   0.023414   0.220    0.826    
## factor(exp)smallt == 0           0.011884   0.025634   0.464    0.643    
## eff_mass:factor(exp)pilot == 0  -0.001268   0.001350  -0.940    0.347    
## eff_mass:factor(exp)smallt == 0 -0.001836   0.001462  -1.256    0.209    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## (Univariate p values reported)

There is an overall effect of mass on peak velocity (slope = -5.043e-02, p = 0.000e+00).

Experiment 2b peak velocity is not different from 2a (p = 6.429e-01).

Experiment 2c peak velocity is not different from 2a (p = 8.259e-01).

The interesting thing with these are the interaction effects.

Experiment 2b peak velocity did NOT change with mass more than 2a. (p = 2.090e-01).

Experiment 2c peak velocity did NOT change with mass more than 2a. (p = 3.474e-01).

Figure 1.5: Peak Velocity by experiment.

Figure 1.6: Peak velocity broken by experiment.

1.4 Reaction Time

Table 1.5: Reaction Time linear models.

Reaction Time	Linear Estimate	P-Value	Std Error
Circle	4.645e-03	0.000e+00	3.305e-04
Pilot	5.313e-03	0.000e+00	3.011e-04
Arc	6.401e-03	0.000e+00	3.341e-04
All	5.461e-03	0.000e+00	1.868e-04

Table 1.5: Reaction time average values (m/s)

Effective Mass (kg)	2a	2b	2c
2.5	0.18±0.012	0.204±0.013	0.198±0.012
3.8	0.186±0.013	0.215±0.013	0.207±0.011
4.7	0.189±0.013	0.219±0.013	0.212±0.012
6.1	0.197±0.013	0.228±0.013	0.216±0.011

This next stat output shows the a LME with movedur ~ target + eff_mass*exp + (1|subj).

## 
##   Simultaneous Tests for General Linear Hypotheses
## 
## Fit: lmer(formula = reaction_tanv ~ factor(targetnum) + eff_mass + 
##     eff_mass * factor(exp) + (1 | subj), data = prefpilot)
## 
## Linear Hypotheses:
##                                   Estimate Std. Error z value Pr(>|z|)    
## (Intercept) == 0                 0.1775709  0.0062008  28.637  < 2e-16 ***
## factor(targetnum)2 == 0         -0.0135552  0.0006985 -19.405  < 2e-16 ***
## factor(targetnum)3 == 0         -0.0002042  0.0007051  -0.290 0.772144    
## factor(targetnum)4 == 0         -0.0204404  0.0006987 -29.256  < 2e-16 ***
## eff_mass == 0                    0.0046670  0.0003561  13.108  < 2e-16 ***
## factor(exp)pilot == 0            0.0169967  0.0079800   2.130 0.033179 *  
## factor(exp)smallt == 0           0.0197597  0.0087367   2.262 0.023717 *  
## eff_mass:factor(exp)pilot == 0   0.0006478  0.0004565   1.419 0.155876    
## eff_mass:factor(exp)smallt == 0  0.0017406  0.0004943   3.521 0.000429 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## (Univariate p values reported)

There is an overall effect of mass on reaction_time (slope = 4.667e-03, p = 0.000e+00).

Experiment 2b reaction_time is significantly greater than 2a (slope = 1.976e-02, p = 2.372e-02).

Experiment 2c reaction_time is significantly greater than 2a (slope = 1.700e-02, p = 3.318e-02).

The interesting thing with these are the interaction effects.

Experiment 2b reaction_time increases with mass more than experiment 2a (slope = 1.741e-03, p = 4.294e-04).

Experiment 2c reaction_time did NOT change with mass more than 2a. (p = 1.559e-01).

Figure 1.7: Reaction Time by experiment.

Figure 1.8: Reaction Time broken by experiment.

1.4.1 Reaction Time Normalized

## boundary (singular) fit: see ?isSingular

Table 1.6: Reaction Time linear models.

Reaction Time Norm	Linear Estimate	P-Value	Std Error
Circle	2.582e-02	0.000e+00	1.871e-03
Pilot	2.748e-02	0.000e+00	1.535e-03
Arc	3.170e-02	0.000e+00	1.654e-03
All	2.833e-02	0.000e+00	9.706e-04

Table 1.6: Reaction time average values (m/s)

Effective Mass (kg)	2a	2b	2c
2.5	1±0.061	1±0.059	1±0.056
3.8	1.039±0.071	1.053±0.062	1.053±0.052
4.7	1.054±0.064	1.071±0.062	1.079±0.053
6.1	1.098±0.062	1.119±0.062	1.099±0.055

This next stat output shows the a LME with movedur ~ target + eff_mass*exp + (1|subj).

## 
##   Simultaneous Tests for General Linear Hypotheses
## 
## Fit: lmer(formula = reaction_tanv_norm ~ factor(targetnum) + eff_mass + 
##     eff_mass * factor(exp) + (1 | subj), data = prefpilot)
## 
## Linear Hypotheses:
##                                   Estimate Std. Error z value Pr(>|z|)    
## (Intercept) == 0                 0.9801391  0.0137450  71.309   <2e-16 ***
## factor(targetnum)2 == 0         -0.0704426  0.0036291 -19.410   <2e-16 ***
## factor(targetnum)3 == 0         -0.0008087  0.0036635  -0.221   0.8253    
## factor(targetnum)4 == 0         -0.1054450  0.0036300 -29.048   <2e-16 ***
## eff_mass == 0                    0.0259603  0.0018499  14.034   <2e-16 ***
## factor(exp)pilot == 0            0.0071271  0.0174362   0.409   0.6827    
## factor(exp)smallt == 0          -0.0103761  0.0190394  -0.545   0.5858    
## eff_mass:factor(exp)pilot == 0   0.0015281  0.0023715   0.644   0.5193    
## eff_mass:factor(exp)smallt == 0  0.0057741  0.0025681   2.248   0.0246 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## (Univariate p values reported)

There is an overall effect of mass on reaction_time (slope = 2.596e-02, p = 0.000e+00).

Experiment 2b reaction_time is not different from 2a (p = 5.858e-01).

Experiment 2c reaction_time is not different from 2a (p = 6.827e-01).

The interesting thing with these are the interaction effects.

Experiment 2b reaction_time did NOT change with mass more than 2a. (p = 2.455e-02).

Experiment 2c reaction_time did NOT change with mass more than 2a. (p = 5.193e-01).

Figure 1.9: Reaction Time by experiment.

Figure 1.10: Reaction Time broken by experiment.

1.4.2 Reaction Velocity

Table 1.7: Reaction Velocity linear models.

Reaction Velocity	Linear Estimate	P-Value	Std Error
Circle	5.994e-05	1.579e-03	1.897e-05
Pilot	8.027e-05	3.342e-02	3.774e-05
Arc	3.659e-05	3.735e-01	4.112e-05
All	5.978e-05	4.338e-03	2.096e-05

Table 1.7: Reaction velocity average values (m/s)

Effective Mass (kg)	2a	2b	2c
2.5	8.951e-04±5.834e-04	-1.554e-04±1.389e-03	-1.621e-04±1.289e-03
3.8	9.981e-04±6.202e-04	-2.193e-04±1.411e-03	-1.224e-04±1.312e-03
4.7	1.051e-03±6.445e-04	5.499e-05±1.494e-03	-3.357e-05±1.272e-03
6.1	1.126e-03±7.045e-04	-7.845e-05±1.556e-03	1.077e-04±1.331e-03

This next stat output shows the a LME with movedur ~ target + eff_mass*exp + (1|subj).

## 
##   Simultaneous Tests for General Linear Hypotheses
## 
## Fit: lmer(formula = reaction_tanvel ~ factor(targetnum) + eff_mass + 
##     eff_mass * factor(exp) + (1 | subj), data = prefpilot)
## 
## Linear Hypotheses:
##                                   Estimate Std. Error z value Pr(>|z|)    
## (Intercept) == 0                 1.161e-03  2.042e-04   5.687 1.30e-08 ***
## factor(targetnum)2 == 0         -1.252e-03  7.837e-05 -15.980  < 2e-16 ***
## factor(targetnum)3 == 0         -4.523e-04  7.912e-05  -5.716 1.09e-08 ***
## factor(targetnum)4 == 0          2.298e-04  7.840e-05   2.931  0.00338 ** 
## eff_mass == 0                    5.310e-05  3.995e-05   1.329  0.18384    
## factor(exp)pilot == 0           -1.179e-03  2.538e-04  -4.645 3.41e-06 ***
## factor(exp)smallt == 0          -1.057e-03  2.761e-04  -3.827  0.00013 ***
## eff_mass:factor(exp)pilot == 0   2.701e-05  5.121e-05   0.527  0.59795    
## eff_mass:factor(exp)smallt == 0 -1.646e-05  5.547e-05  -0.297  0.76671    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## (Univariate p values reported)

There is NOT an overall effect of mass on reaction_ (p = 1.838e-01).

Experiment 2b reaction_ is significantly lower than 2a (slope = -1.057e-03, p = 1.298e-04).

Experiment 2c reaction_ is significantly lower than 2a (slope = -1.179e-03, p = 3.408e-06).

The interesting thing with these are the interaction effects.

Experiment 2b reaction_ decreases with mass more than experiment 2a (slope = -1.646e-05, p = 7.667e-01).

Experiment 2c reaction_ did NOT change with mass more than 2a. (p = 5.979e-01).

Figure 1.11: Reaction by experiment.

Figure 1.12: Reaction broken by experiment.

1.4.3 Reaction Time Algorithm

These next plots are made to try and show the effect of reaciton time algorithms on reaction. Figure 1.13 shows the reaction time by experiment and algorithm. Figure @ref(fig:reactiontanvelalgoplot1} shows the velocity at reaction time by the experiments and algorithms. This plot shows that my algorithm is detecting movement onset at very very low movement speeds, whereas other methods detect it at MUCH higher movement speeds.

Figure 1.13: Reaction Time Algorithm method.

Figure 1.14: Reaction Velocity Algorithm method.

1.5 Reaction Time Percent

Table 1.8: Reaction Time % linear models.

Reaction Time %	Linear Estimate	P-Value	Std Error
Circle	-4.228e-03	0.000e+00	5.030e-04
Pilot	-9.568e-03	0.000e+00	5.142e-04
Arc	-3.117e-03	8.455e-11	4.800e-04
All	-6.171e-03	0.000e+00	2.975e-04

Table 1.8: Reaction % time average values (m/s)

Effective Mass (kg)	2a	2b	2c
2.5	0.242±0.019	0.255±0.02	0.326±0.025
3.8	0.229±0.019	0.249±0.019	0.302±0.019
4.7	0.226±0.017	0.247±0.018	0.297±0.02
6.1	0.225±0.016	0.244±0.017	0.287±0.019

This next stat output shows the a LME with movedur ~ target + eff_mass*exp + (1|subj).

## 
##   Simultaneous Tests for General Linear Hypotheses
## 
## Fit: lmer(formula = reaction_tanv_perc ~ factor(targetnum) + eff_mass + 
##     eff_mass * factor(exp) + (1 | subj), data = prefpilot)
## 
## Linear Hypotheses:
##                                   Estimate Std. Error z value Pr(>|z|)    
## (Intercept) == 0                 0.2509913  0.0109760  22.867  < 2e-16 ***
## factor(targetnum)2 == 0          0.0034694  0.0011106   3.124  0.00178 ** 
## factor(targetnum)3 == 0          0.0012898  0.0011211   1.151  0.24993    
## factor(targetnum)4 == 0         -0.0135542  0.0011108 -12.202  < 2e-16 ***
## eff_mass == 0                   -0.0041829  0.0005661  -7.389 1.48e-13 ***
## factor(exp)pilot == 0            0.0938252  0.0141341   6.638 3.17e-11 ***
## factor(exp)smallt == 0           0.0126124  0.0154761   0.815  0.41509    
## eff_mass:factor(exp)pilot == 0  -0.0053885  0.0007257  -7.425 1.13e-13 ***
## eff_mass:factor(exp)smallt == 0  0.0010706  0.0007859   1.362  0.17310    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## (Univariate p values reported)

There is an overall effect of mass on reaction_time (slope = -4.183e-03, p = 1.477e-13).

Experiment 2b reaction_time is not different from 2a (p = 4.151e-01).

Experiment 2c reaction_time is significantly greater than 2a (slope = 9.383e-02, p = 3.175e-11).

The interesting thing with these are the interaction effects.

Experiment 2b reaction_time increases with mass more than experiment 2a (slope = 1.071e-03, p = 1.731e-01).

Experiment 2c reaction_time decreases with mass more than experiment 2a (slope = -5.389e-03, p = 1.126e-13).

Figure 1.15: Reaction Time by experiment.

Figure 1.16: Reaction Time broken by experiment.

1.6 Endpoint Error

Table 1.9: Miss Distance linear models.

Miss Distance	Linear Estimate	P-Value	Std Error
Circle	-3.925e-05	1.486e-01	2.717e-05
Pilot	1.023e-03	0.000e+00	9.391e-05
Arc	-1.389e-04	8.788e-05	3.541e-05
All	3.740e-04	0.000e+00	4.370e-05

Table 1.9: Miss Distance average values (cm)

Effective Mass (kg)	2a	2b	2c
2.5	0.623±0.094	0.887±0.141	12.712±0.409
3.8	0.611±0.096	0.831±0.129	13.029±0.423
4.7	0.608±0.099	0.857±0.138	13.107±0.419
6.1	0.605±0.098	0.832±0.133	13.08±0.415

This next stat output shows the a LME with miss_dist ~ target + eff_mass*exp + (1|subj).

## 
##   Simultaneous Tests for General Linear Hypotheses
## 
## Fit: lmer(formula = miss_dist ~ factor(targetnum) + eff_mass + eff_mass * 
##     factor(exp) + (1 | subj), data = prefpilot)
## 
## Linear Hypotheses:
##                                   Estimate Std. Error z value Pr(>|z|)    
## (Intercept) == 0                 7.135e-03  2.131e-03   3.348 0.000814 ***
## factor(targetnum)2 == 0         -3.762e-03  1.629e-04 -23.091  < 2e-16 ***
## factor(targetnum)3 == 0          1.503e-03  1.645e-04   9.138  < 2e-16 ***
## factor(targetnum)4 == 0         -3.755e-04  1.630e-04  -2.304 0.021208 *  
## eff_mass == 0                   -5.904e-05  8.305e-05  -0.711 0.477170    
## factor(exp)pilot == 0            1.194e-01  2.748e-03  43.444  < 2e-16 ***
## factor(exp)smallt == 0           2.689e-03  3.009e-03   0.894 0.371434    
## eff_mass:factor(exp)pilot == 0   1.071e-03  1.065e-04  10.059  < 2e-16 ***
## eff_mass:factor(exp)smallt == 0 -8.482e-05  1.153e-04  -0.736 0.461944    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## (Univariate p values reported)

There is NOT an overall effect of mass on endpoint error (p = 4.772e-01).

Experiment 2b endpoint error is not different from 2a (p = 3.714e-01).

Experiment 2c endpoint error is significantly greater than 2a (slope = 1.194e-01, p = 0.000e+00).

The interesting thing with these are the interaction effects.

Experiment 2b endpoint error decreases with mass more than experiment 2a (slope = -8.482e-05, p = 4.619e-01).

Experiment 2c endpoint error increases with mass more than experiment 2a (slope = 1.071e-03, p = 0.000e+00).

Figure 1.17: Miss Distance (cm) by experiment.

(#fig:missdist_normbyexperiment)Movement Duration by experiment.

(#fig:miss_dist11)Miss Distance (cm) broken by experiment.

1.6.1 Endpoint Error Norm

Table 1.10: Miss Distance Norm linear models.

Miss Distance Norm	Linear Estimate	P-Value	Std Error
Circle	-7.070e-03	1.100e-01	4.423e-03
Pilot	8.244e-03	0.000e+00	7.250e-04
Arc	-1.213e-02	2.419e-03	4.000e-03
All	-2.036e-03	2.431e-01	1.744e-03

Table 1.10: Miss Distance Norm average values (cm)

Effective Mass (kg)	2a	2b	2c
2.5	100±14.349	100±14.339	100±2.517
3.8	99.078±15.268	95.227±14.312	102.426±2.782
4.7	97.76±15.234	97.012±14.582	103.228±2.778
6.1	97.495±15.039	94.639±14.417	102.859±2.694

This next stat output shows the a LME with miss_dist_norm ~ target + eff_mass*exp + (1|subj).

## 
##   Simultaneous Tests for General Linear Hypotheses
## 
## Fit: lmer(formula = miss_dist_norm ~ factor(targetnum) + eff_mass + 
##     eff_mass * factor(exp) + (1 | subj), data = prefpilot)
## 
## Linear Hypotheses:
##                                   Estimate Std. Error z value Pr(>|z|)    
## (Intercept) == 0                 0.9854758  0.0222879  44.216  < 2e-16 ***
## factor(targetnum)2 == 0          0.0299250  0.0065186   4.591 4.42e-06 ***
## factor(targetnum)3 == 0          0.0900826  0.0065804  13.690  < 2e-16 ***
## factor(targetnum)4 == 0          0.0064458  0.0065202   0.989 0.322866    
## eff_mass == 0                   -0.0069058  0.0033228  -2.078 0.037680 *  
## factor(exp)pilot == 0           -0.0288586  0.0281584  -1.025 0.305426    
## factor(exp)smallt == 0           0.0007556  0.0307241   0.025 0.980379    
## eff_mass:factor(exp)pilot == 0   0.0149259  0.0042596   3.504 0.000458 ***
## eff_mass:factor(exp)smallt == 0 -0.0050949  0.0046129  -1.104 0.269386    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## (Univariate p values reported)

There is an overall effect of mass on endpoint error (slope = -6.906e-03, p = 3.768e-02).

Experiment 2b endpoint error is not different from 2a (p = 9.804e-01).

Experiment 2c endpoint error is not different from 2a (p = 3.054e-01).

The interesting thing with these are the interaction effects.

Experiment 2b endpoint error did NOT change with mass more than 2a. (p = 2.694e-01).

Experiment 2c endpoint error increases with mass more than experiment 2a (slope = 1.493e-02, p = 4.582e-04).

Figure 1.18: Miss Distance Norm (cm) by experiment.

(#fig:miss_dist_norm11)Miss Distance Norm (cm) broken by experiment.

1.6.2 Miss Average over trials

Table @ref{tab:missavgtrialtab} shows the average values for experiment 2a, 2b, and 2c. These are calculated from a 20 trial window standard deviation, then averaged over all points.

Table 1.11: Average by mass and experiment.

	2a	2b	2c
2.47	0.0062333	0.0088717	0.1272054
3.8	0.0061016	0.0083199	0.1303839
4.7	0.0060759	0.0085774	0.1311127
6.1	0.0060389	0.0083310	0.1308565

Figure 1.19: Miss Dist Average over trials.

1.6.2.1 Stat Miss Average

cftest(lmer(miss_dist_avg ~ eff_mass + trial + factor(exp) + (1|subj),data=prefpilot))

## 
##   Simultaneous Tests for General Linear Hypotheses
## 
## Fit: lmer(formula = miss_dist_avg ~ eff_mass + trial + factor(exp) + 
##     (1 | subj), data = prefpilot)
## 
## Linear Hypotheses:
##                          Estimate Std. Error z value Pr(>|z|)    
## (Intercept) == 0        4.815e-03  1.990e-03   2.420 0.015539 *  
## eff_mass == 0           3.745e-04  1.857e-05  20.170  < 2e-16 ***
## trial == 0             -1.174e-06  3.180e-07  -3.693 0.000222 ***
## factor(exp)pilot == 0   1.238e-01  2.566e-03  48.239  < 2e-16 ***
## factor(exp)smallt == 0  2.258e-03  2.811e-03   0.803 0.421737    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## (Univariate p values reported)

1.6.3 Miss SD over trials

Table @ref{tab:missvartrialtab} shows the average standard deviation values for experiment 2a, 2b, and 2c. These are calculated from a 20 trial window standard deviation, then averaged over all points.

Table 1.12: Average SD by mass and experiment.

	2a	2b	2c
2.47	0.0030362	0.0043348	0.0128198
3.8	0.0030910	0.0041096	0.0132033
4.7	0.0031724	0.0043044	0.0134056
6.1	0.0031148	0.0041577	0.0130635

Table @ref{tab:missvartrialtabmet} shows the average standard deviation values for experiment 1.

Table 1.13: Average Endpoint Error SD for the metabolic experiment

	Speed = 1	Speed = 2	Speed = 3	Speed = 4	Speed = 5	Speed = 6	Speed = 7
2.73 kg	0.0057	0.0045	0.0039	0.0029	0.0028	0.0029	0.003
4.73 kg	0.0065	0.0049	0.0038	0.0036	0.003	0.0033	0.0032
6.99 kg	NaN	0.005	0.0042	0.0035	0.0027	0.0026	0.0034
11.50 kg	NaN	0.0056	0.0044	0.0034	0.0029	0.0028	0.0033

This next plot (fig @ref{fig:missdistvartplot}) shows the standard deviation of miss distance over the trials for every subject and mass.

Figure 1.20: Miss Dist SD over trials.

1.6.3.1 Stat Miss Standard Deviation

cftest(lmer(miss_dist_sd ~ eff_mass + trial + factor(exp) + (1|subj),data=prefpilot))

## 
##   Simultaneous Tests for General Linear Hypotheses
## 
## Fit: lmer(formula = miss_dist_sd ~ eff_mass + trial + factor(exp) + 
##     (1 | subj), data = prefpilot)
## 
## Linear Hypotheses:
##                          Estimate Std. Error z value Pr(>|z|)    
## (Intercept) == 0        3.059e-03  6.190e-04   4.942 7.72e-07 ***
## eff_mass == 0           3.233e-05  8.544e-06   3.784 0.000154 ***
## trial == 0             -3.684e-07  1.463e-07  -2.518 0.011812 *  
## factor(exp)pilot == 0   1.010e-02  7.969e-04  12.677  < 2e-16 ***
## factor(exp)smallt == 0  1.081e-03  8.729e-04   1.238 0.215652    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## (Univariate p values reported)

1.6.3.2 Metabolics

This next plot (fig @ref{fig:missdistvartplotmet}) shows the standard deviation of miss distance over the trials for every subject, mass, and Speed.

## `geom_smooth()` using method = 'loess' and formula 'y ~ x'

Figure 1.21: Miss Dist SD over trials for metabolic experiment.

1.7 Angular Variance

Table 1.14: Miss Distance linear models.

Miss Distance	Linear Estimate	P-Value	Std Error
Circle	9.021e-02	2.331e-01	7.565e-02
Pilot	6.775e-01	7.504e-01	2.130e+00
Arc	-4.072e-01	5.259e-01	6.420e-01
All	1.998e-01	8.294e-01	9.270e-01

Table 1.14: Miss Angle Variance average values (deg^2)

Effective Mass (kg)	2a	2b	2c
2.5	2.988±0.375	19.59±4.591	82.775±14.702
3.8	2.551±0.238	15.455±2.954	92.356±23.995
4.7	3.023±0.299	19.224±4.053	89.809±18.937
6.1	3.212±0.267	17.067±3.091	86.145±16.938

This next stat output shows the a LME with missangle ~ target + eff_mass*exp + (1|subj).

## 
##   Simultaneous Tests for General Linear Hypotheses
## 
## Fit: lmer(formula = missangle ~ eff_mass * factor(exp) + (1 | subj), 
##     data = var_data)
## 
## Linear Hypotheses:
##                                 Estimate Std. Error z value Pr(>|z|)    
## (Intercept) == 0                 2.55856   16.67940   0.153 0.878086    
## eff_mass == 0                    0.09021    1.74656   0.052 0.958807    
## factor(exp)smallt == 0          17.01325   23.58824   0.721 0.470750    
## factor(exp)pilot == 0           82.32164   21.53302   3.823 0.000132 ***
## eff_mass:factor(exp)smallt == 0 -0.49741    2.47000  -0.201 0.840400    
## eff_mass:factor(exp)pilot == 0   0.58730    2.25480   0.260 0.794505    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## (Univariate p values reported)

There is NOT an overall effect of mass on miss angle variance (p = 9.588e-01).

Experiment 2b miss angle variance is not different from 2a (p = 4.707e-01).

Experiment 2c miss angle variance is significantly greater than 2a (slope = 8.232e+01, p = 1.318e-04).

The interesting thing with these are the interaction effects.

Experiment 2b miss angle variance decreases with mass more than experiment 2a (slope = -4.974e-01, p = 8.404e-01).

Experiment 2c miss angle variance did NOT change with mass more than 2a. (p = 7.945e-01).

Figure 1.22: Miss Angle Variance (deg^2) by experiment.

Figure 1.23: Miss Angle Variance (deg^2) broken by experiment.

1.7.1 Angular Miss Average over trials

Table @ref{tab:missangavgtrialtab} shows the average values for experiment 2a, 2b, and 2c. These are calculated from a 20 trial window standard deviation, then averaged over all points.

Table 1.15: Average by mass and experiment.

	2a	2b	2c
2.47	0.1001624	1.0104141	4.249243
3.8	0.1962406	0.9631639	3.719996
4.7	0.1278115	1.0994883	3.805261
6.1	0.0842250	0.7822437	3.690864

Figure 1.24: Miss Angle Average over trials.

1.7.1.1 Stat Miss Angle Average

cftest(lmer(missangle_avg ~ eff_mass + trial + factor(exp) + (1|subj),data=prefpilot))

## 
##   Simultaneous Tests for General Linear Hypotheses
## 
## Fit: lmer(formula = missangle_avg ~ eff_mass + trial + factor(exp) + 
##     (1 | subj), data = prefpilot)
## 
## Linear Hypotheses:
##                          Estimate Std. Error z value Pr(>|z|)    
## (Intercept) == 0        3.591e-01  6.045e-01   0.594   0.5525    
## eff_mass == 0          -6.232e-02  5.811e-03 -10.726  < 2e-16 ***
## trial == 0              2.430e-04  9.952e-05   2.442   0.0146 *  
## factor(exp)pilot == 0   3.822e+00  7.793e-01   4.904 9.38e-07 ***
## factor(exp)smallt == 0  8.500e-01  8.537e-01   0.996   0.3194    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## (Univariate p values reported)

1.7.2 Angular Miss standard deviation over trials

Table @ref{tab:missangvartrialtab} shows the average standard deviation values for experiment 2a, 2b, and 2c. These are calculated from a 20 trial window standard deviation, then averaged over all points.

Table 1.16: Average by mass and experiment.

	2a	2b	2c
2.47	1.662090	3.986924	8.396830
3.8	1.530235	3.645400	8.692422
4.7	1.661973	4.035591	8.750259
6.1	1.712020	3.860505	8.684456

Table @ref{tab:missangvartrialtabmet} shows the average standard deviation values for experiment 1.

Table 1.17: Average Endpoint Error standard deviation for the metabolic experiment

	Speed = 1	Speed = 2	Speed = 3	Speed = 4	Speed = 5	Speed = 6	Speed = 7
2.73 kg	2.0588	2.2745	1.8643	1.5763	1.3719	1.3841	1.5603
4.73 kg	2.5019	2.1617	1.818	1.5901	1.3747	1.5252	1.5685
6.99 kg	NaN	2.1953	1.818	1.6125	1.4368	1.2735	1.3828
11.50 kg	NaN	2.2009	1.9782	1.6805	1.572	1.4188	1.5063

This next plot (fig @ref{fig:missangvartplot}) shows the standard deviation of angular over the trials for every subject and mass.

Figure 1.25: Miss Angle standard deviation over trials.

1.7.2.1 Stat Miss Angle Standard Deviation

cftest(lmer(missangle_sd ~ eff_mass + trial + factor(exp) + (1|subj),data=prefpilot))

## 
##   Simultaneous Tests for General Linear Hypotheses
## 
## Fit: lmer(formula = missangle_sd ~ eff_mass + trial + factor(exp) + 
##     (1 | subj), data = prefpilot)
## 
## Linear Hypotheses:
##                         Estimate Std. Error z value Pr(>|z|)    
## (Intercept) == 0       1.448e+00  6.790e-01   2.133   0.0330 *  
## eff_mass == 0          2.638e-02  4.982e-03   5.296 1.18e-07 ***
## trial == 0             4.787e-04  8.532e-05   5.610 2.02e-08 ***
## factor(exp)pilot == 0  7.140e+00  8.759e-01   8.152 4.44e-16 ***
## factor(exp)smallt == 0 2.296e+00  9.595e-01   2.393   0.0167 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## (Univariate p values reported)

1.7.2.2 Metabolics

This next plot (fig @ref{fig:missangvartplotmet}) shows the standard deviation of miss angle over the trials for every subject, mass, and Speed.

## `geom_smooth()` using method = 'loess' and formula 'y ~ x'

Figure 1.26: Miss angle standard deviation over trials for metabolic experiment.

1.8 Radial Variance

Table 1.18: Miss Distance Radial Variance (cm^2) linear models.

Miss Distance	Linear Estimate	P-Value	Std Error
Circle	-4.307e-03	2.749e-01	3.944e-03
Pilot	2.582e-01	3.343e-03	8.798e-02
Arc	-4.993e-03	8.036e-02	2.855e-03
All	1.080e-01	5.990e-03	3.929e-02

Table 1.18: Miss Radial Variance average values (cm^2)

Effective Mass (kg)	2a	2b	2c
2.5	0.2651±0.0148	0.2339±0.0164	1.4368±0.5526
3.8	0.2529±0.0131	0.2227±0.015	1.9259±0.586
4.7	0.25±0.0142	0.2159±0.0153	2.1909±0.4874
6.1	0.2492±0.0208	0.2162±0.0127	2.369±0.471

This next stat output shows the a LME with miss_rad ~ eff_mass*exp + (1|subj).

## NULL

There is NOT an overall effect of mass on miss radial variance (p = 9.515e-01).

Experiment 2b miss radial variance is not different from 2a (p = 9.668e-01).

Experiment 2c miss radial variance is not different from 2a (p = 3.429e-01).

The interesting thing with these are the interaction effects.

Experiment 2b miss radial variance did NOT change with mass more than 2a. (p = 9.945e-01).

Experiment 2c miss radial variance increases with mass more than experiment 2a (slope = 2.625e-01, p = 4.074e-03).

Figure 1.27: Miss Radial Variance by experiment.

Figure 1.28: Miss Rad Variance (cm^2) broken by experiment.

1.8.1 Radial Miss Average over trials

Table @ref{tab:missradavgtrialtab} shows the average values for experiment 2a, 2b, and 2c. These are calculated from a 20 trial window, then averaged over all points.

Table 1.19: Average by mass and experiment.

	2a	2b	2c
2.47	0.0986310	0.0979616	0.0785736
3.8	0.0985490	0.0980965	0.0811442
4.7	0.0990690	0.0981179	0.0826006
6.1	0.0993256	0.0982913	0.0852493

Figure 1.29: Miss Rad Average over trials.

1.8.1.1 Stat Rad Angle Average

cftest(lmer(miss_rad_avg ~ eff_mass + trial + factor(exp) + (1|subj),data=prefpilot))

## 
##   Simultaneous Tests for General Linear Hypotheses
## 
## Fit: lmer(formula = miss_rad_avg ~ eff_mass + trial + factor(exp) + 
##     (1 | subj), data = prefpilot)
## 
## Linear Hypotheses:
##                          Estimate Std. Error z value Pr(>|z|)    
## (Intercept) == 0        9.531e-02  2.083e-03  45.753  < 2e-16 ***
## eff_mass == 0           8.210e-04  1.478e-05  55.543  < 2e-16 ***
## trial == 0              3.651e-08  2.532e-07   0.144    0.885    
## factor(exp)pilot == 0  -1.623e-02  2.687e-03  -6.041 1.53e-09 ***
## factor(exp)smallt == 0 -7.675e-04  2.944e-03  -0.261    0.794    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## (Univariate p values reported)

1.8.2 Radial Miss standard deviation over trials

Table @ref{tab:missradvartrialtab} shows the average standard deviation values for experiment 2a, 2b, and 2c. These are calculated from a 20 trial window standard deviation, then averaged over all points.

Table 1.20: Average standard deviation by mass and experiment.

	2a	2b	2c
2.47	0.0050490	0.0047508	0.0069068
3.8	0.0049380	0.0046566	0.0094450
4.7	0.0049295	0.0045833	0.0116504
6.1	0.0048226	0.0045860	0.0127107

Table @ref{tab:missradvartrialtabmet} shows the average standard deviation values for experiment 1.

Table 1.21: Average Endpoint Error standard deviation for the metabolic experiment

	Speed = 1	Speed = 2	Speed = 3	Speed = 4	Speed = 5	Speed = 6	Speed = 7
2.73 kg	0.0087	0.0067	0.0057	0.0047	0.0049	0.0049	0.0057
4.73 kg	0.009	0.0066	0.0054	0.0054	0.0049	0.0053	0.0054
6.99 kg	NaN	0.0066	0.0057	0.005	0.0045	0.0044	0.0048
11.50 kg	NaN	0.0074	0.0056	0.0049	0.0046	0.0042	0.0048

This next plot (fig @ref{fig:missradvartplot}) shows the standard deviation of radial miss distance over the trials for every subject and mass.

Figure 1.30: Miss Rad standard deviation over trials.

1.8.2.1 Stat Rad Angle Standard Deviation

cftest(lmer(miss_rad_sd ~ eff_mass + trial + factor(exp) + (1|subj),data=prefpilot))

## 
##   Simultaneous Tests for General Linear Hypotheses
## 
## Fit: lmer(formula = miss_rad_sd ~ eff_mass + trial + factor(exp) + 
##     (1 | subj), data = prefpilot)
## 
## Linear Hypotheses:
##                          Estimate Std. Error z value Pr(>|z|)    
## (Intercept) == 0        2.328e-03  1.482e-03   1.570  0.11635    
## eff_mass == 0           6.351e-04  1.688e-05  37.618  < 2e-16 ***
## trial == 0             -4.816e-07  2.891e-07  -1.666  0.09577 .  
## factor(exp)pilot == 0   5.607e-03  1.910e-03   2.935  0.00333 ** 
## factor(exp)smallt == 0 -3.748e-04  2.093e-03  -0.179  0.85785    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## (Univariate p values reported)

1.8.2.2 Metabolics

This next plot (fig @ref{fig:missradvartplotmet}) shows the standard deviation of miss distance over the trials for every subject, mass, and Speed.

## `geom_smooth()` using method = 'loess' and formula 'y ~ x'

Figure 1.31: Miss Dist standard deviation over trials for metabolic experiment.

1.9 Resample Plots

Figure 1.32: Velocity trajectories by experiment.

1.10 Preferred Experiment Grouped Plots

Figure 1.33: Preferred experiment results.

1.10.1 Normalized

Figure 1.34: Preferred experiment Norm results.

2 Metabolics Experiment

We filtered the metabolic data and removed any trial where the miss distance at endpoint was greater than 10 cm, the movement duration was less than 0.2 seconds, or the reaction time was greater than 0.50 s.This removed 13 out of 15975 original data poitns.

2.0.1 Speed on speed

## Analysis of Variance Table
## 
## Response: movedur
##              Df  Sum Sq Mean Sq    F value Pr(>F)    
## speed         1 1099.40 1099.40 1.0453e+05 <2e-16 ***
## eff_mass2     1    0.01    0.01 6.3430e-01 0.4258    
## Residuals 15959  167.85    0.01                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

## 
##   Simultaneous Tests for General Linear Hypotheses
## 
## Fit: lmer(formula = movedur ~ speed + eff_mass2 + (1 | subj), data = metdata_factor)
## 
## Linear Hypotheses:
##                   Estimate Std. Error z value Pr(>|z|)    
## (Intercept) == 0 2.498e-01  8.172e-03  30.571   <2e-16 ***
## speed == 0       1.544e-01  4.760e-04 324.257   <2e-16 ***
## eff_mass2 == 0   5.641e-06  2.371e-04   0.024    0.981    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## (Univariate p values reported)

2.1 MP Gross

## 
##   Simultaneous Tests for General Linear Hypotheses
## 
## Fit: lmer(formula = log(metpowergross) ~ log(movedur) + effmass2 + 
##     (1 | subject), data = mpdata)
## 
## Linear Hypotheses:
##                    Estimate Std. Error z value Pr(>|z|)    
## (Intercept) == 0   4.561517   0.066021  69.092  < 2e-16 ***
## log(movedur) == 0 -0.766794   0.037690 -20.345  < 2e-16 ***
## effmass2 == 0      0.017373   0.003369   5.156 2.52e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## (Univariate p values reported)

## NULL

Table 2.1: Gross Metabolic power plus/minus standard error for the metabolic experiment

	Speed = 1	Speed = 2	Speed = 3	Speed = 4	Speed = 5	Speed = 6	Speed = 7
2.73 kg	171.9775 ± 18.515	131.625 ± 14.3282	110.1838 ± 5.8343	98.8513 ± 7.9976	105.3988 ± 8.8935	99.835 ± 7.0959	NaN ± NA
4.73 kg	187.4712 ± 17.3187	153.6538 ± 13.0638	126.0213 ± 8.2191	104.4825 ± 6.9769	97.5825 ± 7.3818	97.2367 ± 5.4622	NaN ± NA
6.99 kg	NaN ± NA	185.5288 ± 19.5249	140.2988 ± 11.6277	112.705 ± 6.8381	109.9457 ± 8.6896	98.7512 ± 7.5674	93.9237 ± 7.265
11.50 kg	NaN ± NA	222.0613 ± 24.3934	155.0838 ± 13.5348	117.4025 ± 10.6555	110.285 ± 10.4558	96.8337 ± 5.2816	92.7812 ± 6.6335

Figure 2.1: Gross metabolic power.

Parameter estimates are showing as mean +- standard error. The columns are for without the subject mass coefficient, and with a mass coefficient on the effort model. Subj Mass Coef is the subject mass exponent.

The no_mass_coef model is as follows: \[ \dot{e} = a+\frac{bm^c}{T_m^d} \]

The Subject mass model times a1 is as follows: \[ \dot{e} = a*Body Mass^{f}+\frac{bm^c}{T_m^d} \]

The effective mass model times a1 is as follows: \[ \dot{e} = a*Effective\, Mass^{f}+\frac{bm^c}{T_m^d} \]

Table 2.2: Gross metabolic power coefficients.

	a only	a*subject mass	a*effective mass
a	98.2501±3.0512	22.0844±13.6907	101.4027±7.5926
b	0.864±0.4319	0.8593±0.4234	0.8375±0.4215
c	0.8308±0.0998	0.8247±0.0981	0.8548±0.1107
d	5.8254±0.603	5.8562±0.5956	5.8035±0.6061
f	null	0.2983±0.1232	-0.0187±0.0411
SSE	120872.749595644	116826.723834405	120743.074844557
AIC	1750.832	1746.4653	1752.6313
BIC	1766.9875	1765.852	1772.0179

2.2 MP net

## 
##   Simultaneous Tests for General Linear Hypotheses
## 
## Fit: lmer(formula = log(metpowernet) ~ log(movedur) + effmass2 + (1 | 
##     subject), data = mpdata)
## 
## Linear Hypotheses:
##                   Estimate Std. Error z value Pr(>|z|)    
## (Intercept) == 0   2.85218    0.23454  12.161  < 2e-16 ***
## log(movedur) == 0 -2.37941    0.16610 -14.326  < 2e-16 ***
## effmass2 == 0      0.04912    0.01485   3.308  0.00094 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## (Univariate p values reported)

Table 2.3: Net Metabolic power plus/minus standard error for the metabolic experiment

	Speed = 1	Speed = 2	Speed = 3	Speed = 4	Speed = 5	Speed = 6	Speed = 7
2.73 kg	99.075 ± 17.3755	57.7875 ± 15.0154	36.3125 ± 5.9248	24.9875 ± 6.1351	31.5325 ± 8.1858	27.9333 ± 5.6508	NaN ± NA
4.73 kg	113.7375 ± 18.2929	79.9875 ± 13.8077	52.3875 ± 8.9795	30.8212 ± 5.8168	23.9213 ± 7.2462	24.4667 ± 4.0208	NaN ± NA
6.99 kg	NaN ± NA	111.7875 ± 19.9953	65.4 ± 11.9993	37.8638 ± 7.2397	37.7043 ± 7.8668	23.8963 ± 6.5959	19.0538 ± 6.8651
11.50 kg	NaN ± NA	150.475 ± 22.0585	83.35 ± 13.048	45.6812 ± 10.4043	38.5625 ± 9.4318	25.0825 ± 5.0728	21.0525 ± 5.3099

Figure 2.2: Net metabolic power.

Parameter estimates are showing as mean +- standard error. The columns are for without the subject mass coefficient, and with a mass coefficient on the effort model. Subj Mass Coef is the subject mass exponent.

The no_mass_coef model is as follows: \[ \dot{e} = a+\frac{bm^c}{T_m^d} \]

The Subject mass model times a1 is as follows: \[ \dot{e} = a*Body Mass^{f}+\frac{bm^c}{T_m^d} \]

The effective mass model times a1 is as follows: \[ \dot{e} = a*Effective\, Mass^{f}+\frac{bm^c}{T_m^d} \]

Table 2.4: Net metabolic power coefficients.

	a only	a*subject mass	a*effective mass
a	24.7227±2.9124	0.1006±0.2368	24.0136±7.0228
b	1.0308±0.467	1.0007±0.4474	1.031±0.4707
c	0.7964±0.0904	0.7942±0.089	0.7962±0.1007
d	5.6574±0.5473	5.7151±0.5413	5.6575±0.5519
f	null	1.0939±0.4615	5e-04±0.1585
SSE	105365.400000357	101455.132835216	105365.395173997
AIC	1725.1562	1720.0843	1727.1561
BIC	1741.3117	1739.4709	1746.5428

2.3 MCost Gross

Table 2.5: Gross Metabolic Cost plus/minus standard error for the metabolic experiment

	Speed = 1	Speed = 2	Speed = 3	Speed = 4	Speed = 5	Speed = 6	Speed = 7
2.73 kg	93.3222 ± 8.9748	80.1472 ± 7.2013	82.5764 ± 3.4054	94.0607 ± 9.0851	117.4043 ± 9.7673	125.4443 ± 10.8215	NaN ± NA
4.73 kg	104.3653 ± 7.7764	95.0103 ± 5.6431	96.0467 ± 6.7137	97.5592 ± 7.0411	109.7052 ± 8.5622	123.3466 ± 10.6279	NaN ± NA
6.99 kg	NaN ± NA	108.7596 ± 10.3474	95.2653 ± 7.1374	96.7068 ± 6.2899	113.0375 ± 8.3502	120.2383 ± 9.9578	130.8822 ± 10.7193
11.50 kg	NaN ± NA	134.6313 ± 12.7635	106.7865 ± 8.1232	101.0186 ± 8.5022	112.9603 ± 9.2217	118.1752 ± 7.0501	128.0428 ± 9.1786

Figure 2.3: Gross metabolic cost.

The linear slope of the metabolic minimum is 0.0173807.

The optimal movement durations using the preferred masses are shown below along with the average movement durations.

Table 2.6: Minimum Cost durations for gross metabolic cost.

	Effective Mass (kg)	Minimum Cost (J)	Minimum Cost Duration (s)	Preferred Duraiton (s)
a1	2.471	78.44419	0.6613455	0.7638165
a1	3.800	83.41499	0.7032816	0.8299896
a1	4.700	85.98258	0.7249254	0.8559532
a1	6.100	89.24014	0.7523910	0.8902248

2.4 MCost Net

Table 2.7: Net Metabolic Cost plus/minus standard error for the metabolic experiment

	Speed = 1	Speed = 2	Speed = 3	Speed = 4	Speed = 5	Speed = 6	Speed = 7
2.73 kg	53.1932 ± 8.5657	34.0816 ± 8.4267	26.267 ± 3.4663	23.2311 ± 5.6268	33.9323 ± 8.6921	35.0672 ± 7.0593	NaN ± NA
4.73 kg	62.5789 ± 9.018	48.3557 ± 6.9453	39.0854 ± 6.5272	27.9088 ± 5.0761	25.9021 ± 7.7596	31.196 ± 5.3426	NaN ± NA
6.99 kg	NaN ± NA	65.0537 ± 11.2371	44.2351 ± 7.8498	32.5745 ± 6.4326	38.6832 ± 7.8991	29.137 ± 8.1055	26.4202 ± 9.651
11.50 kg	NaN ± NA	90.9807 ± 11.7824	57.0999 ± 8.418	39.0674 ± 8.6669	38.9813 ± 8.9591	30.4859 ± 6.2224	28.82 ± 7.2275

Figure 2.4: Net metabolic cost.

The optimal movement durations using the preferred masses are shown below along with the average movement durations.

Table 2.8: Minimum Cost durations for net metabolic cost.

	Effective Mass (kg)	Minimum Cost (J)	Minimum Cost Duration (s)	Preferred Duraiton (s)
a1	2.471	25.52908	0.8500727	0.7638165
a1	3.800	27.12511	0.9032332	0.8299896
a1	4.700	27.94902	0.9306663	0.8559532
a1	6.100	28.99388	0.9654625	0.8902248

2.5 Table of Movement Durations

Table 2.9: Movement Duration plus/minus standard error for the metabolic experiment

	Speed = 1	Speed = 2	Speed = 3	Speed = 4	Speed = 5	Speed = 6	Speed = 7
2.73 kg	0.5486 ± 0.014	0.6202 ± 0.0211	0.7576 ± 0.0325	0.951 ± 0.0419	1.1227 ± 0.0476	1.2528 ± 0.04	NaN ± NA
4.73 kg	0.5644 ± 0.0145	0.6295 ± 0.0219	0.7677 ± 0.0355	0.9386 ± 0.0381	1.1305 ± 0.0416	1.2593 ± 0.0459	NaN ± NA
6.99 kg	NaN ± NA	0.5921 ± 0.011	0.6819 ± 0.007	0.8569 ± 0.0082	1.0306 ± 0.0152	1.2143 ± 0.0205	1.3931 ± 0.0269
11.50 kg	NaN ± NA	0.6114 ± 0.0113	0.6931 ± 0.0115	0.8638 ± 0.0102	1.0304 ± 0.0163	1.2184 ± 0.0144	1.38 ± 0.013

2.6 Endpoint Error

## 
##   Simultaneous Tests for General Linear Hypotheses
## 
## Fit: lmer(formula = log(miss_dist) ~ log(movedur) + eff_mass2 + (1 | 
##     subj), data = metdata)
## 
## Linear Hypotheses:
##                    Estimate Std. Error z value Pr(>|z|)    
## (Intercept) == 0  -5.529646   0.058862  -93.94   <2e-16 ***
## log(movedur) == 0 -0.937237   0.017751  -52.80   <2e-16 ***
## eff_mass2 == 0     0.021596   0.001683   12.83   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## (Univariate p values reported)

Table 2.10: Endpoitn Error plus/minus standard error for the metabolic experiment

	Speed = 1	Speed = 2	Speed = 3	Speed = 4	Speed = 5	Speed = 6	Speed = 7
2.73 kg	0.0118 ± 3e-04	0.0084 ± 2e-04	0.0075 ± 2e-04	0.0056 ± 1e-04	0.0047 ± 1e-04	0.0046 ± 1e-04	0.0052 ± 3e-04
4.73 kg	0.0129 ± 4e-04	0.0094 ± 2e-04	0.0075 ± 1e-04	0.0065 ± 1e-04	0.0052 ± 1e-04	0.005 ± 1e-04	0.0055 ± 3e-04
6.99 kg	NaN ± NA	0.0105 ± 2e-04	0.0088 ± 2e-04	0.0065 ± 1e-04	0.0051 ± 1e-04	0.0044 ± 1e-04	0.005 ± 1e-04
11.50 kg	NaN ± NA	0.0122 ± 2e-04	0.0092 ± 2e-04	0.0067 ± 1e-04	0.0053 ± 1e-04	0.0045 ± 1e-04	0.0049 ± 1e-04

## `geom_smooth()` using formula 'y ~ x'
## `geom_smooth()` using formula 'y ~ x'

Figure 2.5: Endpoint Error.

2.7 Angle Variance

## 
##   Simultaneous Tests for General Linear Hypotheses
## 
## Fit: lmer(formula = log(missangle) ~ log(movedur) + eff_mass + (1 | 
##     subj), data = c)
## 
## Linear Hypotheses:
##                    Estimate Std. Error z value Pr(>|z|)    
## (Intercept) == 0   0.724150   0.111106   6.518 7.14e-11 ***
## log(movedur) == 0 -1.140515   0.074456 -15.318  < 2e-16 ***
## eff_mass == 0      0.017424   0.006883   2.532   0.0114 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## (Univariate p values reported)

Table 2.11: Miss Angle Variance plus/minus standard error for the metabolic experiment

	Speed = 1	Speed = 2	Speed = 3	Speed = 4	Speed = 5	Speed = 6	Speed = 7
2.73 kg	1.1816±,0.2404	0.8386±,0.1829	0.7531±,0.1503	0.5641±,0.1087	0.4743±,0.1047	0.4589±,0.1059	0.5233±,0.1061
4.73 kg	1.2879±,0.2579	0.9431±,0.1916	0.7494±,0.1427	0.6479±,0.1403	0.5246±,0.1151	0.5009±,0.1142	0.547±,0.1099
6.99 kg	±,	1.0496±,0.205	0.8785±,0.1597	0.652±,0.1344	0.511±,0.1173	0.4353±,0.0963	0.4983±,0.1196
11.50 kg	±,	1.2156±,0.2198	0.9214±,0.1697	0.6676±,0.1355	0.53±,0.1126	0.452±,0.101	0.493±,0.1126

## `geom_smooth()` using formula 'y ~ x'
## `geom_smooth()` using formula 'y ~ x'

Figure 2.6: Angular miss variance.

2.8 Radial Endpoint Variance

## 
##   Simultaneous Tests for General Linear Hypotheses
## 
## Fit: lmer(formula = log(miss_rad) ~ log(movedur) + eff_mass + (1 | 
##     subj), data = c)
## 
## Linear Hypotheses:
##                     Estimate Std. Error  z value Pr(>|z|)    
## (Intercept) == 0  -10.559873   0.086527 -122.041   <2e-16 ***
## log(movedur) == 0  -1.000083   0.070358  -14.214   <2e-16 ***
## eff_mass == 0      -0.006928   0.006506   -1.065    0.287    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## (Univariate p values reported)

Table 2.12: Radial Endpoint Variance plus/minus standard error for the metabolic experiment

	Speed = 1	Speed = 2	Speed = 3	Speed = 4	Speed = 5	Speed = 6	Speed = 7
2.73 kg	0.3286±,0.0772	0.2452±,0.0943	0.212±,0.056	0.1659±,0.0119	0.1802±,0.0322	0.1666±,0.0096	0.1983±,0.0012
4.73 kg	0.3244±,0.0778	0.2426±,0.0473	0.1943±,0.0302	0.1928±,0.0334	0.1793±,0.023	0.1752±,0.012	0.183±,0.0184
6.99 kg	±,	0.2456±,0.0572	0.2012±,0.0684	0.1834±,0.0723	0.1603±,0.0278	0.1578±,0.014	0.1647±,0.0191
11.50 kg	±,	0.2745±,0.0397	0.1985±,0.013	0.1776±,0.0235	0.1613±,0.0264	0.1564±,0.0164	0.1619±,0.0177

## `geom_smooth()` using formula 'y ~ x'
## `geom_smooth()` using formula 'y ~ x'

Figure 2.7: Radial miss variance.

2.9 Reaction Time

## 
##   Simultaneous Tests for General Linear Hypotheses
## 
## Fit: lmer(formula = reaction_tanv ~ log(movedur) + eff_mass2 + (1 | 
##     subj), data = metdata)
## 
## Linear Hypotheses:
##                    Estimate Std. Error z value Pr(>|z|)    
## (Intercept) == 0  0.1585730  0.0071557   22.16   <2e-16 ***
## log(movedur) == 0 0.0530319  0.0012279   43.19   <2e-16 ***
## eff_mass2 == 0    0.0023967  0.0001164   20.59   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## (Univariate p values reported)

## 
##   Simultaneous Tests for General Linear Hypotheses
## 
## Fit: lmer(formula = reaction_tanv ~ movedur + eff_mass2 + (1 | subj), 
##     data = metdata)
## 
## Linear Hypotheses:
##                   Estimate Std. Error z value Pr(>|z|)    
## (Intercept) == 0 0.0924072  0.0072719   12.71   <2e-16 ***
## movedur == 0     0.0643985  0.0014023   45.92   <2e-16 ***
## eff_mass2 == 0   0.0023962  0.0001155   20.75   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## (Univariate p values reported)

Table 2.13: Reaction time plus/minus standard error for the metabolic experiment

	Speed = 1	Speed = 2	Speed = 3	Speed = 4	Speed = 5	Speed = 6	Speed = 7
2.73 kg	0.1123 ± 0.0028	0.1268 ± 0.002	0.1401 ± 0.0019	0.1547 ± 0.0017	0.1661 ± 0.0018	0.1757 ± 0.0021	0.1931 ± 0.0042
4.73 kg	0.1325 ± 0.0027	0.1344 ± 0.002	0.1445 ± 0.0019	0.1623 ± 0.0016	0.1787 ± 0.0017	0.1922 ± 0.0018	0.2129 ± 0.0051
6.99 kg	NaN ± NA	0.137 ± 0.002	0.1489 ± 0.0018	0.1671 ± 0.0018	0.1759 ± 0.0018	0.1938 ± 0.0019	0.2108 ± 0.0022
11.50 kg	NaN ± NA	0.1446 ± 0.002	0.157 ± 0.0017	0.1699 ± 0.0019	0.1874 ± 0.0017	0.2021 ± 0.0019	0.2259 ± 0.0023

## `geom_smooth()` using formula 'y ~ x'
## `geom_smooth()` using formula 'y ~ x'

Figure 2.8: Reaction time in metabolic experiment.

2.9.0.1 Reaction Time %

## 
##   Simultaneous Tests for General Linear Hypotheses
## 
## Fit: lmer(formula = reaction_tanv_perc ~ log(movedur) + eff_mass2 + 
##     (1 | subj), data = metdata)
## 
## Linear Hypotheses:
##                     Estimate Std. Error z value Pr(>|z|)    
## (Intercept) == 0   0.1563571  0.0092862   16.84   <2e-16 ***
## log(movedur) == 0 -0.1432859  0.0016273  -88.05   <2e-16 ***
## eff_mass2 == 0     0.0028230  0.0001543   18.30   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## (Univariate p values reported)

## 
##   Simultaneous Tests for General Linear Hypotheses
## 
## Fit: lmer(formula = reaction_tanv_perc ~ movedur + eff_mass2 + (1 | 
##     subj), data = metdata)
## 
## Linear Hypotheses:
##                    Estimate Std. Error z value Pr(>|z|)    
## (Intercept) == 0  0.3192568  0.0093404   34.18   <2e-16 ***
## movedur == 0     -0.1536866  0.0019291  -79.67   <2e-16 ***
## eff_mass2 == 0    0.0025781  0.0001589   16.23   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## (Univariate p values reported)

Table 2.14: Reaction time plus/minus standard error for the metabolic experiment

	Speed = 1	Speed = 2	Speed = 3	Speed = 4	Speed = 5	Speed = 6	Speed = 7
2.73 kg	0.236 ± 0.0061	0.2345 ± 0.0039	0.2189 ± 0.0031	0.191 ± 0.0024	0.1667 ± 0.0022	0.1485 ± 0.002	0.1496 ± 0.0046
4.73 kg	0.2633 ± 0.0059	0.2415 ± 0.0038	0.2228 ± 0.0032	0.1982 ± 0.0022	0.1804 ± 0.002	0.1622 ± 0.0017	0.1556 ± 0.0041
6.99 kg	NaN ± NA	0.2458 ± 0.0038	0.2263 ± 0.0028	0.2024 ± 0.0024	0.1758 ± 0.002	0.1643 ± 0.002	0.156 ± 0.0021
11.50 kg	NaN ± NA	0.2519 ± 0.0038	0.2375 ± 0.0029	0.2047 ± 0.0024	0.1877 ± 0.002	0.1716 ± 0.0018	0.1682 ± 0.002

## `geom_smooth()` using formula 'y ~ x'
## `geom_smooth()` using formula 'y ~ x'

Figure 2.9: Reaction time in metabolic experiment.

2.10 Metabolic results plot

Figure 2.10: Metabolic experiment results.

3 Effort models

We compute 4 effort models here. Gross metabolics, net metabolics, and sum of torque squared (experimentally calculated and calcualted from minimum jerk). Net and gross metabolics have been addressed before, here we add sum of torque squared.

Sum of torque sqaured is calcualted from the data and simulated minimum jerk profiles and then fit to an effort model like net metabolic and gross metabolic power but without the a parameter.

\[ \dot{e} = \frac{bm^c}{T_m^d} \]

The parameters fit for the effort models are shown in table @ref(tab:effort_prarms).

3.1 Torque Squared

Figure 3.1: Sum of torque squared fits from the data

3.2 Effort model parameters

This table shows a summary of all the parameters that were fitted in the effort models. SSE, AIC, and BIC can be found in their respective sections.

Table 3.1: Parameters fit in the effort models.

	Net Metabolics	Gross Metabolics	Torque\(^2\)	Torque\(^2\) minjerk
a0	73.3259±3.6041	73.3259±3.6041	0	0
a	24.0346 ± 2.9124	98.2501 ± 3.0512	0	0
b	1.0308 ± 0.467	0.864 ± 0.4319	0.0416 ± 0.0079	0.2885 ± 0.0429
c	0.7964 ± 0.0904	0.8308 ± 0.0998	2.1339 ± 0.0728	1.6071 ± 0.054
d	5.6574 ± 0.5473	5.8254 ± 0.603	3.4951 ± 0.1229	1.3379 ± 0.0249
AIC	1725.15615301424	1750.8320060654	9611.79628744657	35100.9080475733
BIC	1741.31169609851	1766.98754914967	9632.60990953091	35125.7853519489

3.2.1 Torque squared models with offset not forced to 0

Sum of torque sqaured is calcualted from the data and simulated minimum jerk profiles and then fit to an effort model like net metabolic and gross metabolic power. In these we allowed \(a\) to be fit to see if it would predict a 0 offset.

\[ \dot{e} = a+\frac{bm^c}{T_m^d} \]

This table shows the confident intervals on the torque with \(a\) model. The probability of \(a\) (\(a_1\)) being greater than 0 is 4.990231110^{-4}.

Table 3.2: Confidence intervals for torque squared model.

	2.5%	97.5%
a1	-2.6747330	-0.9462295
a2	0.0553365	0.1392793
a3	1.7512603	2.0645923
a4	2.9486703	3.4315542

4 Probablity Modeling

The probability function for the 2a is: \[ ln\left(\frac{P_i}{1-P_i}\right) = \beta_0 + \beta_2 x_2 \] Which leads to \[ P(Success|T) = \frac{1}{1+e^{-(\beta_0) - (\beta_2)T}} \] Mass is removed from this probability as according to the model it is insignificant. Duration nad mass alos condound here, so we only use duration. I leave it \(\beta_2\) because that is more similar to the glm with mass from experiement 1.

We then use this function to first fit an inverse logit to experiment 2a and 2b. We then use the criteria for success and fit the same inverse logit function but using the data from experiment 1.

4.1 Probability of sucess in just 2a and 2b without 1

The following table shows the beta coefficients for the inverse logit function only predicting from experiment 2a and 2b.

Table 4.1: Beta coefficient for the inverse logit function to predict probability of success.

	2a	2b
\(\beta_0\)	2.5791 ± 0.469	1.1985 ± 0.174
\(\beta_2\)	1.6285 ± 0.575	0.4219 ± 0.193

Using these functions we can then predict the probability of success as a fraction of success given the data and using the logit model. The following table shows this for experiment 2a and 2b.

Table 4.2: Success probabilities for experiment 2a and 2b. Also predicted from glm fitted using data from 2a and 2b

	2a	Predicted 2a	2b	Predicted 2b
2.47	0.9782	0.9786	0.8110	0.8243
3.8	0.9839	0.9807	0.8537	0.8278
4.7	0.9779	0.9815	0.8167	0.8293
6.1	0.9815	0.9825	0.8318	0.8324

We can also estimate the probability on the standard deviation of the miss distance.

Table 4.3: Success probabilities for experiment 2a and 2b. Also predicted from glm fitted using data from 2a and 2b. 2b Is off cause i havn’t done the joint probability yet.

	2a	Predicted 2a	2b	Predicted 2b
2.47	0.9782	0.9915	0.8110	0.9915
3.8	0.9839	0.9913	0.8537	0.9913
4.7	0.9779	0.9899	0.8167	0.9899
6.1	0.9815	0.9906	0.8318	0.9906

4.1.1 2a and 2b GLM probability plots

The plot below shows the fits of the glm’s fitted to only data from experiment 2a and 2b. Unfortunately, these glm’s don’t seem to have the same behavior as data fitted to experiment 1 of dropping off to 0 at faster speeds. This is probably due to the lack of really fast or really slow trials so it just predicts a flat line essentially.

Figure 4.1: Probability of success with glm fitted to experiment 2a and 2b data.

4.1.2 Success variability over the experiment

4.1.2.1 2a

The following plot shows the average success (20 trials) of over the trial for experiment 2a.

## 
##   Simultaneous Tests for General Linear Hypotheses
## 
## Fit: lmer(formula = success_avg ~ eff_mass + trial + (1 | subj), data = prefdata)
## 
## Linear Hypotheses:
##                    Estimate Std. Error z value Pr(>|z|)    
## (Intercept) == 0  9.805e-01  6.389e-03 153.454  < 2e-16 ***
## eff_mass == 0     2.714e-04  2.550e-04   1.064    0.287    
## trial == 0       -1.383e-05  2.952e-06  -4.685 2.79e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## (Univariate p values reported)

The following plot shows the variability (20 trials) of over the trial for experiment 2a.

## 
##   Simultaneous Tests for General Linear Hypotheses
## 
## Fit: lmer(formula = success_sd ~ eff_mass + trial + (1 | subj), data = prefdata)
## 
## Linear Hypotheses:
##                   Estimate Std. Error z value Pr(>|z|)    
## (Intercept) == 0 6.782e-02  2.040e-02   3.324 0.000887 ***
## eff_mass == 0    5.902e-04  8.475e-04   0.696 0.486201    
## trial == 0       3.928e-05  9.812e-06   4.003 6.25e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## (Univariate p values reported)

4.1.2.2 2b

The following plot shows the average success (20 trials) of over the trial for experiment 2b.

## 
##   Simultaneous Tests for General Linear Hypotheses
## 
## Fit: lmer(formula = success_avg ~ eff_mass + trial + (1 | subj), data = smalltdata)
## 
## Linear Hypotheses:
##                   Estimate Std. Error z value Pr(>|z|)    
## (Intercept) == 0 8.012e-01  3.445e-02  23.260  < 2e-16 ***
## eff_mass == 0    3.889e-03  8.009e-04   4.856 1.20e-06 ***
## trial == 0       7.673e-05  1.857e-05   4.133 3.58e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## (Univariate p values reported)

The following plot shows the variability (20 trials) of over the trial for experiment 2b.

## 
##   Simultaneous Tests for General Linear Hypotheses
## 
## Fit: lmer(formula = success_sd ~ eff_mass + trial + (1 | subj), data = smalltdata)
## 
## Linear Hypotheses:
##                    Estimate Std. Error z value Pr(>|z|)    
## (Intercept) == 0  3.130e-01  3.975e-02   7.873 3.55e-15 ***
## eff_mass == 0     1.996e-03  8.572e-04   2.329  0.01988 *  
## trial == 0       -5.311e-05  1.987e-05  -2.672  0.00753 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## (Univariate p values reported)

4.1.3 Statistics on probability of success 2a

## 
##   Simultaneous Tests for General Linear Hypotheses
## 
## Fit: lmer(formula = success ~ eff_mass + (1 | subj), data = aggregate(success ~ 
##     eff_mass + subj, prefdata, mean))
## 
## Linear Hypotheses:
##                   Estimate Std. Error z value Pr(>|z|)    
## (Intercept) == 0 0.9781917  0.0089704 109.046   <2e-16 ***
## eff_mass == 0    0.0001357  0.0014250   0.095    0.924    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## (Univariate p values reported)

4.1.4 Statistics on probability of success 2b

## 
##   Simultaneous Tests for General Linear Hypotheses
## 
## Fit: lmer(formula = success ~ eff_mass + (1 | subj), data = aggregate(success ~ 
##     eff_mass + subj, smalltdata, mean))
## 
## Linear Hypotheses:
##                  Estimate Std. Error z value Pr(>|z|)    
## (Intercept) == 0 0.803251   0.046611  17.233   <2e-16 ***
## eff_mass == 0    0.004996   0.007143   0.699    0.484    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## (Univariate p values reported)

4.2 Probability of success using experiment 1

This table shows the beta coefficients when using an inverse logit on experiment 1 trying to predict 2a and 2b.

Table 4.4: Beta coefficient for the inverse logit function to predict probability of success.

	2a	2b
\(\beta_0\)	-1.4458 ± 0.125	-2.9285 ± 0.091
\(\beta_1\)	-0.0966 ± 0.008	-0.0843 ± 0.006
\(\beta_2\)	5.8758 ± 0.188	6.0896 ± 0.129

This plot only includes movement durations that are seen in the metabolic experiment. The black vertical bars show the range of durations for the 2a preferred exerpiement. The red vertical bars show the range of durations for the smallt target.

Figure 4.2: Probability of success given movement duration and mass. The black vertical bars show the range of durations for the 2a preferred exerpiement. The red vertical bars show the range of durations for the smallt target.

This plot includes low and high movement durations to show that the functions converge to 0 and 1 probability respectively.

Figure 4.3: Probability of success given movement duration and mass. The black vertical bars show the range of durations for the 2a preferred exerpiement. The red vertical bars show the range of durations for the smallt target.

This next table shows the movement durations for experiment 2a and 2b, the probability of success from the experiment, along with the probability of success from the logistic regression. The last row is the mean probability.

	2a Movedur	2a Exp Prob	2a Pred Prob	2b Movedur	2b Exp Prob	2b Pred Prob
2.47	0.7638	0.9782	0.9429	0.8226	0.8110	0.8668
3.80	0.8300	0.9839	0.9554	0.8813	0.8537	0.8926
4.70	0.8560	0.9779	0.9581	0.9051	0.8167	0.8991
6.10	0.8902	0.9815	0.9607	0.9588	0.8318	0.9165
Mean	NaN	0.9804	0.9543	NaN	0.8283	0.8937

4.2.1 Success at metabolically optimal

The table (@ref{tab:optdurprob}) shows the metabolically optimal (gross) durations with the predicted probabilites from the glm using experiment 1 and 2a.

Table 4.5: Success probabilites from experiment 2a/1 at the metabolically optimal duraitons.

Effective.Mass	Duration	Success.Prob
2.47	0.6613455	0.9003840
4.73	0.7032816	0.9028780
6.99	0.7249254	0.8945901
11.50	0.7523910	0.8657960

4.2.2 Success Over trials

4.2.2.1 Average Reward over trials

Figure 4.4: Reward average over trials for metabolic experiment.

## 
##   Simultaneous Tests for General Linear Hypotheses
## 
## Fit: lmer(formula = success_2a_avg ~ eff_mass2 + trial + speed + (1 | 
##     subj), data = metdata)
## 
## Linear Hypotheses:
##                    Estimate Std. Error z value Pr(>|z|)    
## (Intercept) == 0  7.275e-01  1.971e-02  36.908  < 2e-16 ***
## eff_mass2 == 0   -7.505e-03  2.675e-04 -28.057  < 2e-16 ***
## trial == 0        6.352e-05  1.768e-05   3.593 0.000327 ***
## speed == 0        5.419e-02  5.805e-04  93.348  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## (Univariate p values reported)

4.2.2.2 Reward Variance over trials

Figure 4.5: Reward standard deviation over trials for metabolic experiment.

## 
##   Simultaneous Tests for General Linear Hypotheses
## 
## Fit: lmer(formula = success_2a_sd ~ eff_mass2 + trial + speed + (1 | 
##     subj), data = metdata)
## 
## Linear Hypotheses:
##                    Estimate Std. Error  z value Pr(>|z|)    
## (Intercept) == 0  4.240e-01  2.388e-02   17.754  < 2e-16 ***
## eff_mass2 == 0    9.910e-03  3.083e-04   32.148  < 2e-16 ***
## trial == 0       -1.281e-04  2.037e-05   -6.289  3.2e-10 ***
## speed == 0       -7.407e-02  6.690e-04 -110.716  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## (Univariate p values reported)

4.3 Predicting movedur off of probability

The probability of reward that minimizes the error of predicted movement durations for the 2a experiment is 0.9498. The table below shows the predicted movement durations and the expected movement durations. The SSE of this prediction is 0.0038674.

Table 4.6: Predicted movement durations for the 2a given probability of: 0.9498

	Effective Mass (kg)	Predicted Duration	Preferred Duration
	2.47	0.787	0.764
	3.8	0.809	0.83
	4.7	0.824	0.856
	6.1	0.847	0.89

The probability of reward that minimizes the error of predicted movement durations for the 2a experiment is 0.8944. The table below shows hte predicted movement durations and the expected movement durations. The SSE of this prediction is 0.0255866.

Table 4.7: Predicted movement durations for the 2b given probability of: 0.8944

	Effective Mass (kg)	Predicted Duration	Preferred Duration
	2.47	0.866	0.823
	3.8	0.885	0.881
	4.7	0.897	0.905
	6.1	0.917	0.959

5 Utility Modeling

5.1 Individual Utility

This plot below shows individual subjects and their utility fits. This uses gross metabolics as the effort term.

The average fitted \(\alpha\) value was 50.3353.

Figure 5.1: Utility fits by subject.

5.2 Utility Code

5.2.1 Combined utility code

5.3 Table for the coefficients in Utility Modeling

We next fitted a utility model by altering \(\alpha\) to try and predict the movement durations seen in 2a,b,c.

The utility function that is fit for these next plots is below. \(T_r\) and \(T_m\) are the reaction time and movement duration. \(P(R|m,t)\) is determined from the section above, probability alpha modeling. \(a\), \(b\), \(c\), \(d\) are determined from the metabolic data. Resting rate is shown by \(a_0\), and \(a_0\) = 73.527. The parameters a, b, c, and d are shown in 3.1.

\[J = \frac{\alpha P(R|m,T_m) -\left( a_0 T_r + a T_m + \frac{bm^c}{T_m^d} \right)}{T_r+T_m}\] Ideally the probability function has an effect of mass in it, but for the following results we use the glm from experiement 2a/2b to fit \(\alpha\), which leads to the probability function only including a term of time.

\[J = \frac{\alpha P(R|T_m) -\left( a_0 T_r + a T_m + \frac{bm^c}{T_m^d} \right)}{T_r+T_m}\]

\(T_r\) and \(T_m\) are the reaction time and movement duration. Using the values from experiment 2a,b,c, we can optimize the error of the prediction by altering \(\alpha\).

The tables below show the movement durations (@ref{tab:utilmovedurstab}), reaction time (@ref{rab:utilreacttimestab}).

Table 5.1: Movement durations by experiement and effective mass used in the Utility model

	2a	2b	2c
2.47 kg	0.764	0.823	0.632
3.80 kg	0.830	0.881	0.703
4.70 kg	0.856	0.905	0.741
6.10 kg	0.890	0.959	0.781

Table 5.2: Reaction times by experiement and effective mass used in the Utility model

	2a	2b	2c
2.47 kg	0.180	0.204	0.198
3.80 kg	0.186	0.215	0.207
4.70 kg	0.189	0.219	0.212
6.10 kg	0.197	0.228	0.216

5.4 Experimental Utility Fits

5.4.1 2a Alpha

This table (??) shows the \(\alpha\) value, predicted durations for the models, and the SSE between that and the experimental data. The SSE for all these models is shown in detail later (section @ref{SSE2a}).

Table 5.3: Preferred duration and predicted durations for each model.

	2a Experiment	Net Metabolic Power	Gross Metabolic power	Utility (Net Power)	Utility (Gross Power	Torque\(^2\)	Torque\(^2\) minjerk
Alpha	0	0	0	83.959	59.335	30.4952	34.6073
2.47	0.7638	0.8543	0.6613	0.775	0.774	0.7	0.72
4.73	0.83	0.9078	0.7033	0.825	0.825	0.78	0.79
6.99	0.856	0.9353	0.7249	0.852	0.852	0.84	0.84
11.50	0.8902	0.9703	0.7524	0.888	0.888	0.94	0.94
SSE	0	2.695e-02	6.272e-02	1.705e-04	1.492e-04	9.304e-03	6.251e-03

The probability of success for utility in experiement 2a using the optimized alpha value are shown below.

Table 5.4: Probability of success used in utility modeling when fitting alpha, Expirement 2a.

	Utility Net	Utility Gross	Utility Torque	Utility Torque Mj
2.47	0.9463080	0.9460087	0.9189840	0.9273136
3.8	0.9541144	0.9541144	0.9410454	0.9442220
4.7	0.9571539	0.9571539	0.9541673	0.9541673
6.1	0.9601764	0.9601764	0.9703501	0.9703501

5.4.2 2b Alpha

This table (5.5) shows the \(\alpha\) value, predicted durations for the models, and the SSE between that and the experimental data. The SSE for all these models is shown in detail later (section @ref{SSE2b}).

Table 5.5: Preferred duration and predicted durations for each model.

	2b Experiment	Net Metabolic Power	Gross Metabolic power	Utility (Net Power)	Utility (Gross Power	Torque\(^2\)	Torque\(^2\) minjerk
Alpha	0	0	0	179.0124	105.7846	80.6792	100.5872
2.47	0.8226	0.8543	0.6613	0.849	0.847	0.84	0.85
4.73	0.8813	0.9078	0.7033	0.884	0.884	0.88	0.88
6.99	0.9051	0.9353	0.7249	0.904	0.906	0.9	0.9
11.50	0.9588	0.9703	0.7524	0.934	0.937	0.94	0.94
SSE	0	2.749e-03	1.328e-01	1.322e-03	1.080e-03	6.850e-04	1.132e-03

The probability of success for utility in experiement 2b using the optimized alpha value are shown below.

Table 5.6: Probability of success used in utility modeling when fitting alpha, Expirement 2b.

	Utility Net	Utility Gross	Utility Torque	Utility Torque Mj
2.47	0.8842438	0.8829914	0.8785148	0.8848657
3.8	0.8941844	0.8941844	0.8918575	0.8918575
4.7	0.8984485	0.8995543	0.8962044	0.8962044
6.1	0.9041941	0.9057650	0.9073128	0.9073128

5.4.3 2c Alpha

This table (5.7) shows the \(\alpha\) value, predicted durations for the models, and the SSE between that and the experimental data. The SSE for all these models is shown in detail later (section @ref{SSE2b}).

Table 5.7: Preferred duration and predicted durations for each model.

	2c Experiment	Net Metabolic Power	Gross Metabolic power	Utility (Net Power)	Utility (Gross Power	Torque\(^2\)	Torque\(^2\) minjerk
Alpha	0	0	0	112.1505	95.6647	26.8914	24.6437
2.47	0.6316	0.8543	0.6613	0.663	0.658	0.42	0.05
4.73	0.7033	0.9078	0.7033	0.713	0.708	0.6	0.14
6.99	0.7412	0.9353	0.7249	0.74	0.734	0.72	0.28
11.50	0.7811	0.9703	0.7524	0.774	0.767	0.91	0.87
SSE	0	1.649e-01	1.972e-03	1.132e-03	9.692e-04	7.251e-02	8.762e-01

The probability of success for utility in experiement 2b using the optimized alpha value are shown below.

Table 5.8: Probability of success used in utility modeling when fitting alpha, Expirement 2c.

	Utility Net	Utility Gross	Utility Torque	Utility Torque Mj
2.47	1	1	1	1
3.8	1	1	1	1
4.7	1	1	1	1
6.1	1	1	1	1

5.5 3 Alpha Fits

This section analysis fits two \(\alpha\) values to experiment 2a and 2b. These next tables show the movement durations, predicted movement durations, the fitted alpha values, and the probabilities of success.

The \(\alpha\) value fitted here is 59.3350329 for 2a, and for 2b is 105.7845779, 0.0010795, and 2c 95.6647265, 9.691655310^{-4}.

The SSE for experiment 2a is 1.492e-04. The SSE for experiment 2b is 1.080e-03. The SSE for experiment 2a/b is 2.159e-03. The SSE for experiment 2c is 9.692e-04.

The total SSE for all 3 is 2.198e-03.

(#tab:combutdurtab1_3alphas)Experimental and predicted movement durations for the experiments.

	2a Exp	2a pred	2b Exp	2b pred	2c Exp	2c pred
2.47	0.7638165	0.774	0.8226259	0.847	0.6316043	0.658
3.8	0.8299896	0.825	0.8812989	0.884	0.7032684	0.708
4.7	0.8559532	0.852	0.9051184	0.906	0.7412180	0.734
6.1	0.8902248	0.888	0.9588485	0.937	0.7810693	0.767

(#tab:combutprobtab1_3alphas)Probabilites of success for the experiments.

	2a	2b	2c
2.47	0.9460	0.8830	1
3.8	0.9541	0.8942	1
4.7	0.9572	0.8996	1
6.1	0.9602	0.9058	1

(#tab:alphtab1_3alphas)Alpha values fitted to experiment 2a/2b, and a seperate alpha for 2c.

	2a	2b	2c
lpha	59.335	105.785	95.665

Figure 5.2: Utility fits across experiments.

5.6 2a and 2b Combined Utility fits

This section analysis fits one \(\alpha\) value to experiment 2a and 2b at the same time. These next tables show the movement durations, predicted movement durations, the fitted alpha values, and the probabilities of success. The \(\alpha\) value for 2a and 2b are fit at once, so it is the same. 2c has its own \(\alpha\) value.

The \(\alpha\) value fitted here is 68.1368242. The SSE for experiment 2a/2b when using one alpha is 5.235e-03. The SSE for experiment 2c is 9.692e-04. The total SSE for all 3 is 6.204e-03.

Table 5.9: Experimental and predicted movement durations for the experiments.

	2a Exp	2a pred	2b Exp	2b pred	2c Exp	2c pred
2.47	0.7638165	0.760	0.8226259	0.870	0.6316043	0.658
3.8	0.8299896	0.809	0.8812989	0.911	0.7032684	0.708
4.7	0.8559532	0.836	0.9051184	0.934	0.7412180	0.734
6.1	0.8902248	0.871	0.9588485	0.966	0.7810693	0.767

Table 5.10: Probabilites of success for the experiments.

	2a	2b	2c
2.47	0.9416	0.8967	1
3.8	0.9498	0.9088	1
4.7	0.9531	0.9139	1
6.1	0.9562	0.9198	1

Table 5.11: Alpha values fitted to experiment 2a/2b, and a seperate alpha for 2c.

	2a	2b	2c
lpha	68.137	68.137	95.665

Figure 5.3: Utility fits across experiments.

5.7 2a Durations

5.7.1 MOdel Plotting Function

5.7.2 DF Creation

5.7.3 Peak Velocity Plotting

5.7.4 SSE of models - Exp 2a

The utility combined alpha is using the alpha value predicted off fitting a utility model to the preferred and small target experiement at the same time. This alpha value is used to make figure ??.

5.7.4.1 Absolute

This table shows the SSE for the 2a movement duration and peak velocity predictions.

Table 5.12: Exp 2a - Sum squared errors for movement duration and peak velocity.

	Model	Movement Duration SSE	Movement Duration AIC	Movement Duration BIC	Peak Velocity SSE	Peak Velocity AIC	Peak Velocity BIC
SSE.2	Accuracy Prob	3.867e-03	-2.58e+01	-2.64e+01	7.421e-04	-3.24e+01	-3.30e+01
SSE.3	Met Cost Gross	6.272e-02	-1.46e+01	-1.52e+01	3.904e-03	-2.57e+01	-2.63e+01
SSE.4	Met Cost Net	2.695e-02	-1.80e+01	-1.86e+01	3.711e-03	-2.59e+01	-2.65e+01
SSE.5	Torque^2	9.304e-03	-2.23e+01	-2.29e+01	2.281e-04	-3.71e+01	-3.77e+01
SSE.7	Utility Gross	1.492e-04	-3.68e+01	-3.80e+01	5.393e-04	-3.16e+01	-3.29e+01
SSE.9	Utility Net	1.705e-04	-3.63e+01	-3.75e+01	5.529e-04	-3.15e+01	-3.28e+01
SSE.10	Utility Gross Combined Alpha	1.223e-03	-2.84e+01	-2.96e+01	3.051e-04	-3.39e+01	-3.52e+01
SSE.11	Utility Net Combined Alpha	3.432e-03	-2.42e+01	-2.55e+01	2.246e-04	-3.51e+01	-3.64e+01

5.7.4.2 Normalized

Table 5.13: Exp 2a - Sum squared errors for NORMALIZED movement duration and peak velocity.

	Model	Movement Duration SSE	Movement Duration AIC	Movement Duration BIC	Peak Velocity SSE	Peak Velocity AIC	Peak Velocity BIC
SSE.2	Accuracy Prob	1.683e-02	-1.99e+01	-2.05e+01	3.270e-02	-1.72e+01	-1.78e+01
SSE.3	Met Cost Gross	1.914e-03	-2.86e+01	-2.92e+01	1.153e-02	-2.14e+01	-2.20e+01
SSE.4	Met Cost Net	2.137e-03	-2.81e+01	-2.88e+01	1.197e-02	-2.12e+01	-2.19e+01
SSE.5	Torque^2	3.852e-02	-1.66e+01	-1.72e+01	4.223e-03	-2.54e+01	-2.60e+01
SSE.7	Utility Gross	1.156e-03	-2.86e+01	-2.98e+01	9.845e-03	-2.00e+01	-2.13e+01
SSE.9	Utility Net	1.329e-03	-2.80e+01	-2.93e+01	1.025e-02	-1.99e+01	-2.11e+01
SSE.10	Utility Gross Combined Alpha	1.295e-03	-2.81e+01	-2.94e+01	1.016e-02	-1.99e+01	-2.11e+01
SSE.11	Utility Net Combined Alpha	1.384e-03	-2.79e+01	-2.91e+01	1.037e-02	-1.98e+01	-2.10e+01

5.7.5 2a Modeling Plot

Figure 5.4: Modeling Results

5.7.6 SSE of models - Exp 2a to 2b

5.7.6.1 Absolute

This table shows the SSE for the 2b movement duration and peak velocity predictions. These SSE’s are calculated from only taking the predicted durations as before, and seeing how they compare to 2b. No new model fitting was done.

Table 5.14: Exp 2b - Sum squared errors for movement duration and peak velocity.

	Model	Movement Duration SSE	Movement Duration AIC	Movement Duration BIC	Peak Velocity SSE	Peak Velocity AIC	Peak Velocity BIC
SSE.2	Accuracy Prob	2.559e-02	-1.82e+01	-1.88e+01	2.639e-03	-2.73e+01	-2.79e+01
SSE.3	Met Cost Gross	1.328e-01	-1.16e+01	-1.22e+01	1.372e-02	-2.07e+01	-2.13e+01
SSE.4	Met Cost Net	2.749e-03	-2.71e+01	-2.77e+01	1.733e-04	-3.82e+01	-3.88e+01
SSE.5	Torque^2	2.989e-02	-1.76e+01	-1.82e+01	3.187e-03	-2.65e+01	-2.72e+01
SSE.7	Utility Gross	1.338e-02	-1.88e+01	-2.00e+01	1.555e-03	-2.74e+01	-2.86e+01
SSE.9	Utility Net	1.328e-02	-1.88e+01	-2.01e+01	1.548e-03	-2.74e+01	-2.87e+01
SSE.10	Utility Gross Combined Alpha	2.164e-02	-1.69e+01	-1.81e+01	2.287e-03	-2.59e+01	-2.71e+01
SSE.11	Utility Net Combined Alpha	2.944e-02	-1.56e+01	-1.69e+01	2.984e-03	-2.48e+01	-2.60e+01

5.7.6.2 Normalized

Table 5.15: Exp 2b - Sum squared errors for NORMALIZED movement duration and peak velocity.

	Model	Movement Duration SSE	Movement Duration AIC	Movement Duration BIC	Peak Velocity SSE	Peak Velocity AIC	Peak Velocity BIC
SSE.2	Accuracy Prob	1.270e-02	-2.10e+01	-2.16e+01	0.000e+00	-Inf	-Inf
SSE.3	Met Cost Gross	8.598e-04	-3.18e+01	-3.24e+01	0.000e+00	-Inf	-Inf
SSE.4	Met Cost Net	1.001e-03	-3.12e+01	-3.18e+01	0.000e+00	-Inf	-Inf
SSE.5	Torque^2	4.321e-02	-1.61e+01	-1.67e+01	0.000e+00	-Inf	-Inf
SSE.7	Utility Gross	3.649e-04	-3.32e+01	-3.44e+01	0.000e+00	-Inf	-Inf
SSE.9	Utility Net	4.388e-04	-3.25e+01	-3.37e+01	0.000e+00	-Inf	-Inf
SSE.10	Utility Gross Combined Alpha	4.289e-04	-3.26e+01	-3.38e+01	0.000e+00	-Inf	-Inf
SSE.11	Utility Net Combined Alpha	4.573e-04	-3.23e+01	-3.35e+01	0.000e+00	-Inf	-Inf

5.7.7 SSE of models - Exp 2a to 2c

5.7.7.1 Absolute

This table shows the SSE for the 2c movement duration and peak velocity predictions. These SSE’s are calculated from only taking the predicted durations as before, and seeing how they compare to 2b. No new model fitting was done.

Table 5.16: Exp 2c - Sum squared errors for movement duration and peak velocity.

	Model	Movement Duration SSE	Movement Duration AIC	Movement Duration BIC	Peak Velocity SSE	Peak Velocity AIC	Peak Velocity BIC
SSE.2	Accuracy Prob	4.653e-02	-1.58e+01	-1.64e+01	5.754e-02	-1.50e+01	-1.56e+01
SSE.3	Met Cost Gross	1.972e-03	-2.85e+01	-2.91e+01	2.861e-02	-1.78e+01	-1.84e+01
SSE.4	Met Cost Net	1.649e-01	-1.08e+01	-1.14e+01	8.275e-02	-1.35e+01	-1.41e+01
SSE.5	Torque^2	4.558e-02	-1.59e+01	-1.65e+01	5.282e-02	-1.53e+01	-1.59e+01
SSE.7	Utility Gross	5.880e-02	-1.29e+01	-1.41e+01	6.104e-02	-1.27e+01	-1.40e+01
SSE.9	Utility Net	5.909e-02	-1.29e+01	-1.41e+01	6.114e-02	-1.27e+01	-1.40e+01
SSE.10	Utility Gross Combined Alpha	4.474e-02	-1.40e+01	-1.52e+01	5.687e-02	-1.30e+01	-1.42e+01
SSE.11	Utility Net Combined Alpha	3.517e-02	-1.49e+01	-1.62e+01	5.362e-02	-1.32e+01	-1.45e+01

5.7.7.2 Normalized

Table 5.17: Exp 2c - Sum squared errors for NORMALIZED movement duration and peak velocity.

	Model	Movement Duration SSE	Movement Duration AIC	Movement Duration BIC	Peak Velocity SSE	Peak Velocity AIC	Peak Velocity BIC
SSE.2	Accuracy Prob	4.905e-02	-1.56e+01	-1.62e+01	0.000e+00	-Inf	-Inf
SSE.3	Met Cost Gross	1.829e-02	-1.95e+01	-2.02e+01	0.000e+00	-Inf	-Inf
SSE.4	Met Cost Net	1.899e-02	-1.94e+01	-2.00e+01	0.000e+00	-Inf	-Inf
SSE.5	Torque^2	1.198e-02	-2.12e+01	-2.19e+01	0.000e+00	-Inf	-Inf
SSE.7	Utility Gross	1.554e-02	-1.82e+01	-1.94e+01	0.000e+00	-Inf	-Inf
SSE.9	Utility Net	1.615e-02	-1.80e+01	-1.93e+01	0.000e+00	-Inf	-Inf
SSE.10	Utility Gross Combined Alpha	1.602e-02	-1.81e+01	-1.93e+01	0.000e+00	-Inf	-Inf
SSE.11	Utility Net Combined Alpha	1.633e-02	-1.80e+01	-1.92e+01	0.000e+00	-Inf	-Inf

5.8 2b Durations

5.8.1 DF Creation

5.8.2 Peak Velocity Plotting

5.8.3 SSE of models - Exp 2b

The utility combined alpha is using the alpha value predicted off fitting a utility model to the preferred and small target experiement at the same time. This alpha value is used to make figure ??.

5.8.3.1 Absolute

This table shows the SSE for the 2b movement duration and peak velocity predictions.

Table 5.18: Exp 2b - Sum squared errors for movement duration and peak velocity.

	Model	Movement Duration SSE	Movement Duration AIC	Movement Duration BIC	Peak Velocity SSE	Peak Velocity AIC	Peak Velocity BIC
SSE.2	Accuracy Prob	2.559e-02	-1.82e+01	-1.88e+01	2.639e-03	-2.73e+01	-2.79e+01
SSE.3	Met Cost Gross	1.328e-01	-1.16e+01	-1.22e+01	1.372e-02	-2.07e+01	-2.13e+01
SSE.4	Met Cost Net	2.749e-03	-2.71e+01	-2.77e+01	1.733e-04	-3.82e+01	-3.88e+01
SSE.5	Torque^2	2.989e-02	-1.76e+01	-1.82e+01	3.187e-03	-2.65e+01	-2.72e+01
SSE.7	Utility Gross	1.080e-03	-2.89e+01	-3.01e+01	3.433e-04	-3.35e+01	-3.47e+01
SSE.9	Utility Net	1.322e-03	-2.81e+01	-2.93e+01	3.775e-04	-3.31e+01	-3.43e+01
SSE.10	Utility Gross Combined Alpha	2.164e-02	-1.69e+01	-1.81e+01	2.287e-03	-2.59e+01	-2.71e+01
SSE.11	Utility Net Combined Alpha	2.944e-02	-1.56e+01	-1.69e+01	2.984e-03	-2.48e+01	-2.60e+01

5.8.3.2 Normalized

Table 5.19: Exp 2a - Sum squared errors for NORMALIZED movement duration and peak velocity.

	Model	Movement Duration SSE	Movement Duration AIC	Movement Duration BIC	Peak Velocity SSE	Peak Velocity AIC	Peak Velocity BIC
SSE.2	Accuracy Prob	1.270e-02	-2.10e+01	-2.16e+01	2.639e-02	-1.81e+01	-1.87e+01
SSE.3	Met Cost Gross	8.598e-04	-3.18e+01	-3.24e+01	8.069e-03	-2.28e+01	-2.34e+01
SSE.4	Met Cost Net	1.001e-03	-3.12e+01	-3.18e+01	8.438e-03	-2.26e+01	-2.33e+01
SSE.5	Torque^2	4.321e-02	-1.61e+01	-1.67e+01	5.508e-03	-2.44e+01	-2.50e+01
SSE.7	Utility Gross	5.223e-03	-2.26e+01	-2.38e+01	1.616e-02	-1.80e+01	-1.93e+01
SSE.9	Utility Net	6.453e-03	-2.17e+01	-2.29e+01	1.796e-02	-1.76e+01	-1.89e+01
SSE.10	Utility Gross Combined Alpha	4.289e-04	-3.26e+01	-3.38e+01	6.873e-03	-2.15e+01	-2.27e+01
SSE.11	Utility Net Combined Alpha	4.573e-04	-3.23e+01	-3.35e+01	7.022e-03	-2.14e+01	-2.26e+01

5.8.4 2b Modeling Plot

Figure 5.5: Modeling Results

5.8.5 SSE of models - Exp 2b to 2a

5.8.5.1 Absolute

This table shows the SSE for the 2b movement duration and peak velocity predictions. These SSE’s are calculated from only taking the predicted durations as before, and seeing how they compare to 2b. No new model fitting was done.

Table 5.20: Exp 2b - Sum squared errors for movement duration and peak velocity.

	Model	Movement Duration SSE	Movement Duration AIC	Movement Duration BIC	Peak Velocity SSE	Peak Velocity AIC	Peak Velocity BIC
SSE.2	Accuracy Prob	3.867e-03	-2.58e+01	-2.64e+01	7.421e-04	-3.24e+01	-3.30e+01
SSE.3	Met Cost Gross	6.272e-02	-1.46e+01	-1.52e+01	3.904e-03	-2.57e+01	-2.63e+01
SSE.4	Met Cost Net	2.695e-02	-1.80e+01	-1.86e+01	3.711e-03	-2.59e+01	-2.65e+01
SSE.5	Torque^2	9.304e-03	-2.23e+01	-2.29e+01	2.281e-04	-3.71e+01	-3.77e+01
SSE.7	Utility Gross	1.453e-02	-1.85e+01	-1.97e+01	2.774e-03	-2.51e+01	-2.63e+01
SSE.9	Utility Net	1.440e-02	-1.85e+01	-1.97e+01	2.786e-03	-2.51e+01	-2.63e+01
SSE.10	Utility Gross Combined Alpha	1.223e-03	-2.84e+01	-2.96e+01	3.051e-04	-3.39e+01	-3.52e+01
SSE.11	Utility Net Combined Alpha	3.432e-03	-2.42e+01	-2.55e+01	2.246e-04	-3.51e+01	-3.64e+01

5.8.5.2 Normalized

Table 5.21: Exp 2b - Sum squared errors for NORMALIZED movement duration and peak velocity.

	Model	Movement Duration SSE	Movement Duration AIC	Movement Duration BIC	Peak Velocity SSE	Peak Velocity AIC	Peak Velocity BIC
SSE.2	Accuracy Prob	1.683e-02	-1.99e+01	-2.05e+01	3.270e-02	-1.72e+01	-1.78e+01
SSE.3	Met Cost Gross	1.914e-03	-2.86e+01	-2.92e+01	1.153e-02	-2.14e+01	-2.20e+01
SSE.4	Met Cost Net	2.137e-03	-2.81e+01	-2.88e+01	1.197e-02	-2.12e+01	-2.19e+01
SSE.5	Torque^2	3.852e-02	-1.66e+01	-1.72e+01	4.223e-03	-2.54e+01	-2.60e+01
SSE.7	Utility Gross	7.952e-03	-2.09e+01	-2.21e+01	2.115e-02	-1.70e+01	-1.82e+01
SSE.9	Utility Net	9.455e-03	-2.02e+01	-2.14e+01	2.320e-02	-1.66e+01	-1.78e+01
SSE.10	Utility Gross Combined Alpha	1.295e-03	-2.81e+01	-2.94e+01	1.016e-02	-1.99e+01	-2.11e+01
SSE.11	Utility Net Combined Alpha	1.384e-03	-2.79e+01	-2.91e+01	1.037e-02	-1.98e+01	-2.10e+01

5.8.6 SSE of models - Exp 2b to 2c

5.8.6.1 Absolute

This table shows the SSE for the 2c movement duration and peak velocity predictions. These SSE’s are calculated from only taking the predicted durations as before, and seeing how they compare to 2b. No new model fitting was done.

Table 5.22: Exp 2c - Sum squared errors for movement duration and peak velocity.

	Model	Movement Duration SSE	Movement Duration AIC	Movement Duration BIC	Peak Velocity SSE	Peak Velocity AIC	Peak Velocity BIC
SSE.2	Accuracy Prob	4.653e-02	-1.58e+01	-1.64e+01	5.754e-02	-1.50e+01	-1.56e+01
SSE.3	Met Cost Gross	1.972e-03	-2.85e+01	-2.91e+01	2.861e-02	-1.78e+01	-1.84e+01
SSE.4	Met Cost Net	1.649e-01	-1.08e+01	-1.14e+01	8.275e-02	-1.35e+01	-1.41e+01
SSE.5	Torque^2	4.558e-02	-1.59e+01	-1.65e+01	5.282e-02	-1.53e+01	-1.59e+01
SSE.7	Utility Gross	1.305e-01	-9.69e+00	-1.09e+01	7.724e-02	-1.18e+01	-1.30e+01
SSE.9	Utility Net	1.298e-01	-9.71e+00	-1.09e+01	7.716e-02	-1.18e+01	-1.30e+01
SSE.10	Utility Gross Combined Alpha	4.474e-02	-1.40e+01	-1.52e+01	5.687e-02	-1.30e+01	-1.42e+01
SSE.11	Utility Net Combined Alpha	3.517e-02	-1.49e+01	-1.62e+01	5.362e-02	-1.32e+01	-1.45e+01

5.8.6.2 Normalized

Table 5.23: Exp 2c - Sum squared errors for NORMALIZED movement duration and peak velocity.

	Model	Movement Duration SSE	Movement Duration AIC	Movement Duration BIC	Peak Velocity SSE	Peak Velocity AIC	Peak Velocity BIC
SSE.2	Accuracy Prob	4.905e-02	-1.56e+01	-1.62e+01	3.596e-02	-1.68e+01	-1.75e+01
SSE.3	Met Cost Gross	1.829e-02	-1.95e+01	-2.02e+01	1.351e-02	-2.08e+01	-2.14e+01
SSE.4	Met Cost Net	1.899e-02	-1.94e+01	-2.00e+01	1.399e-02	-2.06e+01	-2.12e+01
SSE.5	Torque^2	1.198e-02	-2.12e+01	-2.19e+01	3.523e-03	-2.61e+01	-2.68e+01
SSE.7	Utility Gross	3.266e-02	-1.52e+01	-1.65e+01	2.379e-02	-1.65e+01	-1.77e+01
SSE.9	Utility Net	3.569e-02	-1.49e+01	-1.61e+01	2.596e-02	-1.61e+01	-1.74e+01
SSE.10	Utility Gross Combined Alpha	1.602e-02	-1.81e+01	-1.93e+01	1.203e-02	-1.92e+01	-2.05e+01
SSE.11	Utility Net Combined Alpha	1.633e-02	-1.80e+01	-1.92e+01	1.225e-02	-1.92e+01	-2.04e+01

5.9 2c Durations

5.9.1 DF Creation

5.9.2 Peak Velocity Plotting

5.9.3 SSE of models - Exp 2c

The utility combined alpha is using the alpha value predicted off fitting a utility model to the preferred and small target experiement at the same time. This alpha value is used to make figure ??.

5.9.3.1 Absolute

This table shows the SSE for the 2b movement duration and peak velocity predictions.

Table 5.24: Exp 2b - Sum squared errors for movement duration and peak velocity.

	Model	Movement Duration SSE	Movement Duration AIC	Movement Duration BIC	Peak Velocity SSE	Peak Velocity AIC	Peak Velocity BIC
SSE.2	Accuracy Prob	4.653e-02	-1.58e+01	-1.64e+01	5.754e-02	-1.50e+01	-1.56e+01
SSE.3	Met Cost Gross	1.972e-03	-2.85e+01	-2.91e+01	2.861e-02	-1.78e+01	-1.84e+01
SSE.4	Met Cost Net	1.649e-01	-1.08e+01	-1.14e+01	8.275e-02	-1.35e+01	-1.41e+01
SSE.5	Torque^2	4.558e-02	-1.59e+01	-1.65e+01	5.282e-02	-1.53e+01	-1.59e+01
SSE.7	Utility Gross	9.692e-04	-2.93e+01	-3.05e+01	2.972e-02	-1.56e+01	-1.68e+01
SSE.9	Utility Net	1.132e-03	-2.87e+01	-2.99e+01	3.115e-02	-1.54e+01	-1.66e+01
SSE.10	Utility Gross Combined Alpha	4.474e-02	-1.40e+01	-1.52e+01	5.687e-02	-1.30e+01	-1.42e+01
SSE.11	Utility Net Combined Alpha	3.517e-02	-1.49e+01	-1.62e+01	5.362e-02	-1.32e+01	-1.45e+01

5.9.3.2 Normalized

Table 5.25: Exp 2a - Sum squared errors for NORMALIZED movement duration and peak velocity.

	Model	Movement Duration SSE	Movement Duration AIC	Movement Duration BIC	Peak Velocity SSE	Peak Velocity AIC	Peak Velocity BIC
SSE.2	Accuracy Prob	4.905e-02	-1.56e+01	-1.62e+01	3.596e-02	-1.68e+01	-1.75e+01
SSE.3	Met Cost Gross	1.829e-02	-1.95e+01	-2.02e+01	1.351e-02	-2.08e+01	-2.14e+01
SSE.4	Met Cost Net	1.899e-02	-1.94e+01	-2.00e+01	1.399e-02	-2.06e+01	-2.12e+01
SSE.5	Torque^2	1.198e-02	-2.12e+01	-2.19e+01	3.523e-03	-2.61e+01	-2.68e+01
SSE.7	Utility Gross	9.813e-03	-2.00e+01	-2.13e+01	7.732e-03	-2.10e+01	-2.22e+01
SSE.9	Utility Net	9.535e-03	-2.02e+01	-2.14e+01	7.583e-03	-2.11e+01	-2.23e+01
SSE.10	Utility Gross Combined Alpha	1.602e-02	-1.81e+01	-1.93e+01	1.203e-02	-1.92e+01	-2.05e+01
SSE.11	Utility Net Combined Alpha	1.633e-02	-1.80e+01	-1.92e+01	1.225e-02	-1.92e+01	-2.04e+01

5.9.4 2c Modeling Plot

Figure 5.6: Modeling Results

5.9.5 SSE of models - Exp 2c to 2a

5.9.5.1 Absolute

This table shows the SSE for the 2b movement duration and peak velocity predictions. These SSE’s are calculated from only taking the predicted durations as before, and seeing how they compare to 2b. No new model fitting was done.

Table 5.26: Exp 2b - Sum squared errors for movement duration and peak velocity.

	Model	Movement Duration SSE	Movement Duration AIC	Movement Duration BIC	Peak Velocity SSE	Peak Velocity AIC	Peak Velocity BIC
SSE.2	Accuracy Prob	3.867e-03	-2.58e+01	-2.64e+01	7.421e-04	-3.24e+01	-3.30e+01
SSE.3	Met Cost Gross	6.272e-02	-1.46e+01	-1.52e+01	3.904e-03	-2.57e+01	-2.63e+01
SSE.4	Met Cost Net	2.695e-02	-1.80e+01	-1.86e+01	3.711e-03	-2.59e+01	-2.65e+01
SSE.5	Torque^2	9.304e-03	-2.23e+01	-2.29e+01	2.281e-04	-3.71e+01	-3.77e+01
SSE.7	Utility Gross	5.614e-02	-1.31e+01	-1.43e+01	3.321e-03	-2.44e+01	-2.56e+01
SSE.9	Utility Net	5.080e-02	-1.35e+01	-1.47e+01	2.867e-03	-2.50e+01	-2.62e+01
SSE.10	Utility Gross Combined Alpha	1.223e-03	-2.84e+01	-2.96e+01	3.051e-04	-3.39e+01	-3.52e+01
SSE.11	Utility Net Combined Alpha	3.432e-03	-2.42e+01	-2.55e+01	2.246e-04	-3.51e+01	-3.64e+01

5.9.5.2 Normalized

Table 5.27: Exp 2b - Sum squared errors for NORMALIZED movement duration and peak velocity.

	Model	Movement Duration SSE	Movement Duration AIC	Movement Duration BIC	Peak Velocity SSE	Peak Velocity AIC	Peak Velocity BIC
SSE.2	Accuracy Prob	1.683e-02	-1.99e+01	-2.05e+01	3.270e-02	-1.72e+01	-1.78e+01
SSE.3	Met Cost Gross	1.914e-03	-2.86e+01	-2.92e+01	1.153e-02	-2.14e+01	-2.20e+01
SSE.4	Met Cost Net	2.137e-03	-2.81e+01	-2.88e+01	1.197e-02	-2.12e+01	-2.19e+01
SSE.5	Torque^2	3.852e-02	-1.66e+01	-1.72e+01	4.223e-03	-2.54e+01	-2.60e+01
SSE.7	Utility Gross	1.397e-04	-3.71e+01	-3.83e+01	6.245e-03	-2.18e+01	-2.31e+01
SSE.9	Utility Net	1.497e-04	-3.68e+01	-3.80e+01	6.109e-03	-2.19e+01	-2.32e+01
SSE.10	Utility Gross Combined Alpha	1.295e-03	-2.81e+01	-2.94e+01	1.016e-02	-1.99e+01	-2.11e+01
SSE.11	Utility Net Combined Alpha	1.384e-03	-2.79e+01	-2.91e+01	1.037e-02	-1.98e+01	-2.10e+01

5.9.6 SSE of models - Exp 2c to 2b

5.9.6.1 Absolute

This table shows the SSE for the 2c movement duration and peak velocity predictions. These SSE’s are calculated from only taking the predicted durations as before, and seeing how they compare to 2b. No new model fitting was done.

Table 5.28: Exp 2c - Sum squared errors for movement duration and peak velocity.

	Model	Movement Duration SSE	Movement Duration AIC	Movement Duration BIC	Peak Velocity SSE	Peak Velocity AIC	Peak Velocity BIC
SSE.2	Accuracy Prob	4.653e-02	-1.58e+01	-1.64e+01	5.754e-02	-1.50e+01	-1.56e+01
SSE.3	Met Cost Gross	1.972e-03	-2.85e+01	-2.91e+01	2.861e-02	-1.78e+01	-1.84e+01
SSE.4	Met Cost Net	1.649e-01	-1.08e+01	-1.14e+01	8.275e-02	-1.35e+01	-1.41e+01
SSE.5	Torque^2	4.558e-02	-1.59e+01	-1.65e+01	5.282e-02	-1.53e+01	-1.59e+01
SSE.7	Utility Gross	9.692e-04	-2.93e+01	-3.05e+01	2.972e-02	-1.56e+01	-1.68e+01
SSE.9	Utility Net	1.132e-03	-2.87e+01	-2.99e+01	3.115e-02	-1.54e+01	-1.66e+01
SSE.10	Utility Gross Combined Alpha	4.474e-02	-1.40e+01	-1.52e+01	5.687e-02	-1.30e+01	-1.42e+01
SSE.11	Utility Net Combined Alpha	3.517e-02	-1.49e+01	-1.62e+01	5.362e-02	-1.32e+01	-1.45e+01

5.9.6.2 Normalized

Table 5.29: Exp 2c - Sum squared errors for NORMALIZED movement duration and peak velocity.

	Model	Movement Duration SSE	Movement Duration AIC	Movement Duration BIC	Peak Velocity SSE	Peak Velocity AIC	Peak Velocity BIC
SSE.2	Accuracy Prob	4.905e-02	-1.56e+01	-1.62e+01	3.596e-02	-1.68e+01	-1.75e+01
SSE.3	Met Cost Gross	1.829e-02	-1.95e+01	-2.02e+01	1.351e-02	-2.08e+01	-2.14e+01
SSE.4	Met Cost Net	1.899e-02	-1.94e+01	-2.00e+01	1.399e-02	-2.06e+01	-2.12e+01
SSE.5	Torque^2	1.198e-02	-2.12e+01	-2.19e+01	3.523e-03	-2.61e+01	-2.68e+01
SSE.7	Utility Gross	9.813e-03	-2.00e+01	-2.13e+01	7.732e-03	-2.10e+01	-2.22e+01
SSE.9	Utility Net	9.535e-03	-2.02e+01	-2.14e+01	7.583e-03	-2.11e+01	-2.23e+01
SSE.10	Utility Gross Combined Alpha	1.602e-02	-1.81e+01	-1.93e+01	1.203e-02	-1.92e+01	-2.05e+01
SSE.11	Utility Net Combined Alpha	1.633e-02	-1.80e+01	-1.92e+01	1.225e-02	-1.92e+01	-2.04e+01